diff --git a/ext/CatalystStructuralIdentifiabilityExtension.jl b/ext/CatalystStructuralIdentifiabilityExtension.jl
index 58fece8ac5..026fbe6122 100644
--- a/ext/CatalystStructuralIdentifiabilityExtension.jl
+++ b/ext/CatalystStructuralIdentifiabilityExtension.jl
@@ -2,7 +2,7 @@ module CatalystStructuralIdentifiabilityExtension
 
 # Fetch packages.
 using Catalyst
-import StructuralIdentifiability
+import StructuralIdentifiability as SI
 
 # Creates and exports hc_steady_states function.
 include("CatalystStructuralIdentifiabilityExtension/structural_identifiability_extension.jl")
diff --git a/ext/CatalystStructuralIdentifiabilityExtension/structural_identifiability_extension.jl b/ext/CatalystStructuralIdentifiabilityExtension/structural_identifiability_extension.jl
index 561fa388ee..44f7ad9aad 100644
--- a/ext/CatalystStructuralIdentifiabilityExtension/structural_identifiability_extension.jl
+++ b/ext/CatalystStructuralIdentifiabilityExtension/structural_identifiability_extension.jl
@@ -18,77 +18,121 @@ rs = @reaction_network begin
     (p,d), 0 <--> X
 end
 si_ode(rs; measured_quantities = [:X], known_p = [:p])
+
+Notes:
+This function is part of the StructuralIdentifiability.jl extension. StructuralIdentifiability.jl must be imported to access it.
 ```
 """
-function Catalyst.make_si_ode(rs::ReactionSystem; measured_quantities = [], known_p = [], ignore_no_measured_warn=false, remove_conserved = true)
+function Catalyst.make_si_ode(rs::ReactionSystem; measured_quantities = [], known_p = [], 
+                              ignore_no_measured_warn=false, remove_conserved = true)
+    # Creates a MTK ODESystem, and a list of measured quantities (there are equations).
+    # Gives these to SI to create an SI ode model of its preferred form.
     osys, conseqs, _ = make_osys(rs; remove_conserved)
     measured_quantities = make_measured_quantities(rs, measured_quantities, known_p, conseqs; ignore_no_measured_warn)
-    return StructuralIdentifiability.preprocess_ode(osys, measured_quantities)[1]
+    return SI.preprocess_ode(osys, measured_quantities)[1]
 end
 
 ### Structural Identifiability Wrappers ###
 
-# Local identifiability.
-function StructuralIdentifiability.assess_local_identifiability(rs::ReactionSystem, args...; measured_quantities = Num[], known_p = Num[], funcs_to_check = Vector(), remove_conserved = true, ignore_no_measured_warn=false, kwargs...)
+# Creates dispatch for SI's local identifiability analysis function.
+function SI.assess_local_identifiability(rs::ReactionSystem, args...; measured_quantities = Num[], 
+                                         known_p = Num[], funcs_to_check = Vector(), remove_conserved = true, 
+                                         ignore_no_measured_warn=false, kwargs...)
+    # Creates a ODESystem, list of measured quantities, and functions to check, of SI's preferred form.
     osys, conseqs, vars = make_osys(rs; remove_conserved)
     measured_quantities = make_measured_quantities(rs, measured_quantities, known_p, conseqs; ignore_no_measured_warn)
     funcs_to_check = make_ftc(funcs_to_check, conseqs, vars)
-    out = StructuralIdentifiability.assess_local_identifiability(osys, args...; measured_quantities, funcs_to_check, kwargs...)
+
+    # Computes identifiability and converts it to a easy to read form.
+    out = SI.assess_local_identifiability(osys, args...; measured_quantities, funcs_to_check, kwargs...)
     return make_output(out, funcs_to_check, reverse.(conseqs))
 end
 
-# Global identifiability.
-function StructuralIdentifiability.assess_identifiability(rs::ReactionSystem, args...; measured_quantities = Num[], known_p = Num[], funcs_to_check = Vector(), remove_conserved = true, ignore_no_measured_warn=false, kwargs...)
+# Creates dispatch for SI's global identifiability analysis function.
+function SI.assess_identifiability(rs::ReactionSystem, args...; measured_quantities = Num[], known_p = Num[], 
+                                   funcs_to_check = Vector(), remove_conserved = true, ignore_no_measured_warn=false, 
+                                   kwargs...)
+    # Creates a ODESystem, list of measured quantities, and functions to check, of SI's preferred form.
     osys, conseqs, vars = make_osys(rs; remove_conserved)
     measured_quantities = make_measured_quantities(rs, measured_quantities, known_p, conseqs; ignore_no_measured_warn)
     funcs_to_check = make_ftc(funcs_to_check, conseqs, vars)
-    out = StructuralIdentifiability.assess_identifiability(osys, args...; measured_quantities, funcs_to_check, kwargs...)
+
+    # Computes identifiability and converts it to a easy to read form.
+    out = SI.assess_identifiability(osys, args...; measured_quantities, funcs_to_check, kwargs...)
     return make_output(out, funcs_to_check, reverse.(conseqs))
 end
 
-# Identifiable functions.
-function StructuralIdentifiability.find_identifiable_functions(rs::ReactionSystem, args...; measured_quantities = Num[], known_p = Num[], remove_conserved = true, ignore_no_measured_warn=false, kwargs...)
-    osys, conseqs, vars = make_osys(rs; remove_conserved)
+# Creates dispatch for SI's function to find all identifiable functions.
+function SI.find_identifiable_functions(rs::ReactionSystem, args...; measured_quantities = Num[], 
+                                        known_p = Num[], remove_conserved = true, ignore_no_measured_warn=false, 
+                                        kwargs...)
+    # Creates a ODESystem, and list of measured quantities, of SI's preferred form.
+    osys, conseqs = make_osys(rs; remove_conserved)
     measured_quantities = make_measured_quantities(rs, measured_quantities, known_p, conseqs; ignore_no_measured_warn)
-    out = StructuralIdentifiability.find_identifiable_functions(osys, args...; measured_quantities, kwargs...)
+
+    # Computes identifiable functions and converts it to a easy to read form.
+    out = SI.find_identifiable_functions(osys, args...; measured_quantities, kwargs...)
     return vector_subs(out, reverse.(conseqs))
 end
 
 ### Helper Functions ###
 
-# From a reaction system, creates the corresponding ODESystem for SI application (and also compute the, later needed, conservation law equations and list of system symbols).
+# From a reaction system, creates the corresponding MTK-style ODESystem for SI application 
+# Also compute the, later needed, conservation law equations and list of system symbols (states and parameters).
 function make_osys(rs::ReactionSystem; remove_conserved=true)
-    rs = Catalyst.expand_registered_functions(rs)
+    # Creates the ODESystem corresponding to the ReactionSystem (expanding functions and flattening it).
+    # Creates a list of the systems all symbols (states and parameters).
+    rs = Catalyst.expand_registered_functions(flatten(rs))
     osys = convert(ODESystem, rs; remove_conserved)
     vars = [states(rs); parameters(rs)]
 
-    # Fixes conservation law equations. These cannot be computed for hierarchical systems (and hence this is skipped). If none is found, still have to put on the right form.
-    if !isempty(Catalyst.get_systems(rs)) || !remove_conserved
+    # Computes equations for system conservation laws.
+    # These cannot be computed for hierarchical systems (and hence this is skipped). 
+    # If there are no conserved equations, the `conseqs` variable must still have the `Vector{Pair{Any, Any}}` type.
+    if !remove_conserved
         conseqs = Vector{Pair{Any, Any}}[]
     else
         conseqs = [ceq.lhs => ceq.rhs for ceq in conservedequations(rs)]
         isempty(conseqs) && (conseqs = Vector{Pair{Any, Any}}[])
     end
+
     return osys, conseqs, vars
 end
 
-# For input measured quantities, if this is not a vector of equations, convert it to a proper form.
-function make_measured_quantities(rs::ReactionSystem, measured_quantities::Vector{T}, known_p::Vector{S}, conseqs; ignore_no_measured_warn=false) where {T,S}
-    ignore_no_measured_warn || isempty(measured_quantities) && @warn "No measured quantity provided to the `measured_quantities` argument, any further identifiability analysis will likely fail. You can disable this warning by setting `ignore_no_measured_warn=true`."
-    all_quantities = [measured_quantities; known_p]
-    all_quantities = [(quant isa Symbol) ? Catalyst._symbol_to_var(rs, quant) : quant for quant in all_quantities]
-    all_quantities = vector_subs(all_quantities, conseqs)
-    @variables t (___internal_observables(t))[1:length(all_quantities)]
-    return Equation[(all_quantities[i] isa Equation) ? all_quantities[i] : (___internal_observables[i] ~ all_quantities[i]) for i in 1:length(all_quantities)] 
+# Creates a list of measured quantities of a form that SI can read.
+# Each measured quantity must have a form like:
+# `obs_var ~ X` # (Here, `obs_var` is a variable, and X is whatever we can measure).
+function make_measured_quantities(rs::ReactionSystem, measured_quantities::Vector{T}, known_p::Vector{S},
+                                  conseqs; ignore_no_measured_warn=false) where {T,S}
+    # Warning if the user didn't give any measured quantities.
+    if ignore_no_measured_warn || isempty(measured_quantities) 
+        @warn "No measured quantity provided to the `measured_quantities` argument, any further identifiability analysis will likely fail. You can disable this warning by setting `ignore_no_measured_warn=true`."
+    end
+
+    # Appends the known parameters to the measured_quantities vector. Converts any Symbols to symbolics.
+    measured_quantities = [measured_quantities; known_p]
+    measured_quantities = [(q isa Symbol) ? Catalyst._symbol_to_var(rs, q) : q for q in measured_quantities]
+    measured_quantities = vector_subs(measured_quantities, conseqs)
+
+    # Creates one internal observation variable for each measured quantity (`___internal_observables`).
+    # Creates a vector of equations, setting each measured quantity equal to one observation variable.
+    @variables t (___internal_observables(t))[1:length(measured_quantities)]
+    return Equation[(q isa Equation) ? q : (___internal_observables[i] ~ q) for (i,q) in enumerate(measured_quantities)] 
 end
 
-# Creates the functions that we wish to check for identifiability (if none give, by default, a list of parameters and species). Also replaces conservation law equations in.
+# Creates the functions that we wish to check for identifiability.
+# If no `funcs_to_check` are given, defaults to checking identifiability for all states and parameters.
+# Also, for conserved equations, replaces these in (creating a system without conserved quantities).
+# E.g. for `X1 <--> X2`, replaces `X2` with `Γ[1] - X2`.
+# Removing conserved quantities makes SI's algorithms much more performant.
 function make_ftc(funcs_to_check, conseqs, vars)
     isempty(funcs_to_check) && (funcs_to_check = vars)
     return vector_subs(funcs_to_check, conseqs)
 end
 
-# Replaces conservation law equations back in the output, and also sorts it according to their input order (defaults to [states; parameters] order).
+# Processes the outputs to a better form.
+# Replaces conservation law equations back in the output (so that e.g. Γ are not displayed).
+# Sorts the output according to their input order (defaults to the `[states; parameters]` order).
 function make_output(out, funcs_to_check, conseqs)
     funcs_to_check = vector_subs(funcs_to_check, conseqs)
     out = Dict(zip(vector_subs(keys(out), conseqs), values(out)))
@@ -96,5 +140,5 @@ function make_output(out, funcs_to_check, conseqs)
     return out    
 end
 
-# For a vector of expressions and a conservation law, replaces the law in.
+# For a vector of expressions and a conservation law, substitutes the law into every equation.
 vector_subs(eqs, subs) = [substitute(eq, subs) for eq in eqs]
\ No newline at end of file
diff --git a/test/extensions/structural_identifiability.jl b/test/extensions/structural_identifiability.jl
index c8e80bd4c7..6d1a5d4931 100644
--- a/test/extensions/structural_identifiability.jl
+++ b/test/extensions/structural_identifiability.jl
@@ -101,6 +101,7 @@ let
 end
 
 # Tests on a made-up reaction network with mix of identifiable and non-identifiable components.
+# Tests for system with conserved quantity.
 # Tests for symbolics known_p
 # Tests using an equation for measured quantity.
 let 
@@ -184,6 +185,58 @@ let
     make_si_ode(gw_osc_complt; measured_quantities=[gw_osc_complt.M*gw_osc_complt.E])
 end
 
+# Tests for hierarchical model with conservation laws at both top and internal levels.
+let
+    # Identifiability analysis for Catalyst model.
+    rs1 = @reaction_network rn1 begin
+        (k1, k2), X1 <--> X2
+    end
+    rs2 = @reaction_network rn2 begin
+        (k3, k4), X3 <--> X4
+    end
+    @named rs_catalyst = flatten(compose(rs1, [rs2]))
+    @unpack X1, X2, k1, k2 = rn1
+    gi_1 = assess_identifiability(rs_catalyst; measured_quantities=[X1, X2, rs2.X3], known_p=[k1])
+    li_1 = assess_local_identifiability(rs_catalyst; measured_quantities=[X1, X2, rs2.X3], known_p=[k1])
+    ifs_1 = find_identifiable_functions(rs_catalyst; measured_quantities=[X1, X2, rs2.X3], known_p=[k1])
+
+    # Identifiability analysis for Catalyst converted to StructuralIdentifiability.jl model.
+    rs_ode = make_si_ode(rs_catalyst; measured_quantities=[X1, X2, rs2.X3], known_p=[k1])
+    gi_2 = assess_identifiability(rs_ode)
+    li_2 = assess_local_identifiability(rs_ode)
+    ifs_2 = find_identifiable_functions(rs_ode)
+
+    # Identifiability analysis for StructuralIdentifiability.jl model (declare this overwrites e.g. X2 variable etc.).
+    rs_si = @ODEmodel(
+        X1'(t) = -k1*X1(t) + k2*X2(t), 
+        X2'(t) = k1*X1(t) - k2*X2(t),
+        rn2₊X3'(t) = -rn2₊k3*rn2₊X3(t) + rn2₊k4*rn2₊X4(t), 
+        rn2₊X4'(t) = rn2₊k3*rn2₊X3(t) - rn2₊k4*rn2₊X4(t),
+        y1(t) = X1,
+        y2(t) = X2,
+        y3(t) = rn2₊X3,
+        y4(t) = k1
+    )
+    gi_3 = assess_identifiability(rs_si)
+    li_3 = assess_local_identifiability(rs_si)
+    ifs_3 = find_identifiable_functions(rs_si)
+        
+    # Check outputs.
+    @test sym_dict(gi_1) == sym_dict(gi_3)
+    @test sym_dict(li_1) == sym_dict(li_3)
+    @test length(ifs_1)-2 == length(ifs_2)-2 == length(ifs_3) # In the first case, the conservation law parameter is also identifiable.
+
+    # Checks output for the SI converted version of the catalyst model.
+    # For nested systems with conservation laws, conserved quantities like Γ[1], cannot be replaced back.
+    # Hence, here you display identifiability for `Γ[1]` instead of X2.
+    gi_1_no_cq = filter(x -> !occursin("X2",String(x[1])) && !occursin("X4",String(x[1])), sym_dict(gi_1))
+    gi_2_no_cq = filter(x -> !occursin("Γ",String(x[1])), sym_dict(gi_2))
+    li_1_no_cq = filter(x -> !occursin("X2",String(x[1])) && !occursin("X4",String(x[1])), sym_dict(li_1))
+    li_2_no_cq = filter(x -> !occursin("Γ",String(x[1])), sym_dict(li_2))
+    @test gi_1_no_cq == gi_2_no_cq
+    @test li_1_no_cq == li_2_no_cq
+end
+
 # Tests directly on reaction systems with known identifiability structures.
 # Test provided by Alexander Demin.
 let
@@ -236,6 +289,5 @@ let
         :x2 => :globally,
         :x3 => :globally,
     )
-    # Will probably be fixed in the 0.5 release of SI.jl
-    @test_broken find_identifiable_functions(rs, measured_quantities = [:x3])
+    @test length(find_identifiable_functions(rs, measured_quantities = [:x3])) == 1
 end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 90cf6aab4b..cd2b6550e3 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -54,5 +54,6 @@ using SafeTestsets
     ### Tests extensions. ###
     @time @safetestset "BifurcationKit Extension" begin include("extensions/bifurcation_kit.jl") end
     @time @safetestset "HomotopyContinuation Extension" begin include("extensions/homotopy_continuation.jl") end
-        @time @safetestset "Structural Identifiability Extension" begin include("extensions/structural_identifiability.jl") end
+    @time @safetestset "Structural Identifiability Extension" begin include("extensions/structural_identifiability.jl") end
+    
 end # @time