diff --git a/ext/MTKChainRulesCoreExt.jl b/ext/MTKChainRulesCoreExt.jl
index e7019e25df..f84690e23f 100644
--- a/ext/MTKChainRulesCoreExt.jl
+++ b/ext/MTKChainRulesCoreExt.jl
@@ -2,14 +2,99 @@ module MTKChainRulesCoreExt
 
 import ModelingToolkit as MTK
 import ChainRulesCore
-import ChainRulesCore: NoTangent
+import ChainRulesCore: Tangent, ZeroTangent, NoTangent, zero_tangent, unthunk
 
 function ChainRulesCore.rrule(::Type{MTK.MTKParameters}, tunables, args...)
     function mtp_pullback(dt)
+        dt = unthunk(dt)
         (NoTangent(), dt.tunable[1:length(tunables)],
             ntuple(_ -> NoTangent(), length(args))...)
     end
     MTK.MTKParameters(tunables, args...), mtp_pullback
 end
 
+function subset_idxs(idxs, portion, template)
+    ntuple(Val(length(template))) do subi
+        [Base.tail(idx.idx) for idx in idxs if idx.portion == portion && idx.idx[1] == subi]
+    end
+end
+
+selected_tangents(::NoTangent, _) = ()
+selected_tangents(::ZeroTangent, _) = ZeroTangent()
+function selected_tangents(
+        tangents::AbstractArray{T}, idxs::Vector{Tuple{Int}}) where {T <: Number}
+    selected_tangents(tangents, map(only, idxs))
+end
+function selected_tangents(tangents::AbstractArray{T}, idxs...) where {T <: Number}
+    newtangents = copy(tangents)
+    view(newtangents, idxs...) .= zero(T)
+    newtangents
+end
+function selected_tangents(
+        tangents::AbstractVector{T}, idxs) where {S <: Number, T <: AbstractArray{S}}
+    newtangents = copy(tangents)
+    for i in idxs
+        j, k... = i
+        if k == ()
+            newtangents[j] = zero(newtangents[j])
+        else
+            newtangents[j] = selected_tangents(newtangents[j], k...)
+        end
+    end
+    newtangents
+end
+function selected_tangents(tangents::AbstractVector{T}, idxs) where {T <: AbstractArray}
+    newtangents = similar(tangents, Union{T, NoTangent})
+    copyto!(newtangents, tangents)
+    for i in idxs
+        j, k... = i
+        if k == ()
+            newtangents[j] = NoTangent()
+        else
+            newtangents[j] = selected_tangents(newtangents[j], k...)
+        end
+    end
+    newtangents
+end
+function selected_tangents(
+        tangents::Union{Tangent{<:Tuple}, Tangent{T, <:Tuple}}, idxs) where {T}
+    ntuple(Val(length(tangents))) do i
+        selected_tangents(tangents[i], idxs[i])
+    end
+end
+
+function ChainRulesCore.rrule(
+        ::typeof(MTK.remake_buffer), indp, oldbuf::MTK.MTKParameters, idxs, vals)
+    if idxs isa AbstractSet
+        idxs = collect(idxs)
+    end
+    idxs = map(idxs) do i
+        i isa MTK.ParameterIndex ? i : MTK.parameter_index(indp, i)
+    end
+    newbuf = MTK.remake_buffer(indp, oldbuf, idxs, vals)
+    tunable_idxs = reduce(
+        vcat, (idx.idx for idx in idxs if idx.portion isa MTK.SciMLStructures.Tunable))
+    disc_idxs = subset_idxs(idxs, MTK.SciMLStructures.Discrete(), oldbuf.discrete)
+    const_idxs = subset_idxs(idxs, MTK.SciMLStructures.Constants(), oldbuf.constant)
+    nn_idxs = subset_idxs(idxs, MTK.NONNUMERIC_PORTION, oldbuf.nonnumeric)
+
+    pullback = let idxs = idxs
+        function remake_buffer_pullback(buf′)
+            buf′ = unthunk(buf′)
+            f′ = NoTangent()
+            indp′ = NoTangent()
+
+            tunable = selected_tangents(buf′.tunable, tunable_idxs)
+            discrete = selected_tangents(buf′.discrete, disc_idxs)
+            constant = selected_tangents(buf′.constant, const_idxs)
+            nonnumeric = selected_tangents(buf′.nonnumeric, nn_idxs)
+            oldbuf′ = Tangent{typeof(oldbuf)}(; tunable, discrete, constant, nonnumeric)
+            idxs′ = NoTangent()
+            vals′ = map(i -> MTK._ducktyped_parameter_values(buf′, i), idxs)
+            return f′, indp′, oldbuf′, idxs′, vals′
+        end
+    end
+    newbuf, pullback
+end
+
 end
diff --git a/src/systems/index_cache.jl b/src/systems/index_cache.jl
index 3f2b4ddebe..64e9c134f6 100644
--- a/src/systems/index_cache.jl
+++ b/src/systems/index_cache.jl
@@ -288,11 +288,7 @@ function IndexCache(sys::AbstractSystem)
 end
 
 function SymbolicIndexingInterface.is_variable(ic::IndexCache, sym)
-    if sym isa Symbol
-        sym = get(ic.symbol_to_variable, sym, nothing)
-        sym === nothing && return false
-    end
-    return check_index_map(ic.unknown_idx, sym) !== nothing
+    variable_index(ic, sym) !== nothing
 end
 
 function SymbolicIndexingInterface.variable_index(ic::IndexCache, sym)
@@ -300,18 +296,17 @@ function SymbolicIndexingInterface.variable_index(ic::IndexCache, sym)
         sym = get(ic.symbol_to_variable, sym, nothing)
         sym === nothing && return nothing
     end
-    return check_index_map(ic.unknown_idx, sym)
+    idx = check_index_map(ic.unknown_idx, sym)
+    idx === nothing || return idx
+    iscall(sym) && operation(sym) == getindex || return nothing
+    args = arguments(sym)
+    idx = variable_index(ic, args[1])
+    idx === nothing && return nothing
+    return idx[args[2:end]...]
 end
 
 function SymbolicIndexingInterface.is_parameter(ic::IndexCache, sym)
-    if sym isa Symbol
-        sym = get(ic.symbol_to_variable, sym, nothing)
-        sym === nothing && return false
-    end
-    return check_index_map(ic.tunable_idx, sym) !== nothing ||
-           check_index_map(ic.discrete_idx, sym) !== nothing ||
-           check_index_map(ic.constant_idx, sym) !== nothing ||
-           check_index_map(ic.nonnumeric_idx, sym) !== nothing
+    parameter_index(ic, sym) !== nothing
 end
 
 function SymbolicIndexingInterface.parameter_index(ic::IndexCache, sym)
@@ -331,17 +326,21 @@ function SymbolicIndexingInterface.parameter_index(ic::IndexCache, sym)
         ParameterIndex(SciMLStructures.Constants(), idx, validate_size)
     elseif (idx = check_index_map(ic.nonnumeric_idx, sym)) !== nothing
         ParameterIndex(NONNUMERIC_PORTION, idx, validate_size)
-    else
-        nothing
+    elseif iscall(sym) && operation(sym) == getindex
+        args = arguments(sym)
+        pidx = parameter_index(ic, args[1])
+        pidx === nothing && return nothing
+        if pidx.portion == SciMLStructures.Tunable()
+            ParameterIndex(pidx.portion, reshape(pidx.idx, size(args[1]))[args[2:end]...],
+                pidx.validate_size)
+        else
+            ParameterIndex(pidx.portion, (pidx.idx..., args[2:end]...), pidx.validate_size)
+        end
     end
 end
 
 function SymbolicIndexingInterface.is_timeseries_parameter(ic::IndexCache, sym)
-    if sym isa Symbol
-        sym = get(ic.symbol_to_variable, sym, nothing)
-        sym === nothing && return false
-    end
-    return check_index_map(ic.discrete_idx, sym) !== nothing
+    timeseries_parameter_index(ic, sym) !== nothing
 end
 
 function SymbolicIndexingInterface.timeseries_parameter_index(ic::IndexCache, sym)
@@ -350,8 +349,13 @@ function SymbolicIndexingInterface.timeseries_parameter_index(ic::IndexCache, sy
         sym === nothing && return nothing
     end
     idx = check_index_map(ic.discrete_idx, sym)
+    idx === nothing ||
+        return ParameterTimeseriesIndex(idx.clock_idx, (idx.buffer_idx, idx.idx_in_clock))
+    iscall(sym) && operation(sym) == getindex || return nothing
+    args = arguments(sym)
+    idx = timeseries_parameter_index(ic, args[1])
     idx === nothing && return nothing
-    return ParameterTimeseriesIndex(idx.clock_idx, (idx.buffer_idx, idx.idx_in_clock))
+    ParameterIndex(idx.portion, (idx.idx..., args[2:end]...), idx.validate_size)
 end
 
 function check_index_map(idxmap, sym)
diff --git a/src/systems/parameter_buffer.jl b/src/systems/parameter_buffer.jl
index 95ca13adad..ad001b32dc 100644
--- a/src/systems/parameter_buffer.jl
+++ b/src/systems/parameter_buffer.jl
@@ -336,14 +336,15 @@ function Base.copy(p::MTKParameters)
 end
 
 function SymbolicIndexingInterface.parameter_values(p::MTKParameters, pind::ParameterIndex)
+    _ducktyped_parameter_values(p, pind)
+end
+function _ducktyped_parameter_values(p, pind::ParameterIndex)
     @unpack portion, idx = pind
     if portion isa SciMLStructures.Tunable
         return idx isa Int ? p.tunable[idx] : view(p.tunable, idx)
     end
     i, j, k... = idx
-    if portion isa SciMLStructures.Tunable
-        return isempty(k) ? p.tunable[i][j] : p.tunable[i][j][k...]
-    elseif portion isa SciMLStructures.Discrete
+    if portion isa SciMLStructures.Discrete
         return isempty(k) ? p.discrete[i][j] : p.discrete[i][j][k...]
     elseif portion isa SciMLStructures.Constants
         return isempty(k) ? p.constant[i][j] : p.constant[i][j][k...]
@@ -435,8 +436,12 @@ function validate_parameter_type(ic::IndexCache, p, idx::ParameterIndex, val)
 end
 
 function validate_parameter_type(ic::IndexCache, idx::ParameterIndex, val)
+    stype = get_buffer_template(ic, idx).type
+    if idx.portion == SciMLStructures.Tunable() && !(idx.idx isa Int)
+        stype = AbstractArray{<:stype}
+    end
     validate_parameter_type(
-        ic, get_buffer_template(ic, idx).type, Symbolics.Unknown(), nothing, idx, val)
+        ic, stype, Symbolics.Unknown(), nothing, idx, val)
 end
 
 function validate_parameter_type(ic::IndexCache, stype, sz, sym, index, val)
@@ -444,11 +449,13 @@ function validate_parameter_type(ic::IndexCache, stype, sz, sym, index, val)
     # Nonnumeric parameters have to match the type
     if portion === NONNUMERIC_PORTION
         val isa stype && return nothing
-        throw(ParameterTypeException(:validate_parameter_type, sym, stype, val))
+        throw(ParameterTypeException(
+            :validate_parameter_type, sym === nothing ? index : sym, stype, val))
     end
     # Array parameters need array values...
     if stype <: AbstractArray && !isa(val, AbstractArray)
-        throw(ParameterTypeException(:validate_parameter_type, sym, stype, val))
+        throw(ParameterTypeException(
+            :validate_parameter_type, sym === nothing ? index : sym, stype, val))
     end
     # ... and must match sizes
     if stype <: AbstractArray && sz != Symbolics.Unknown() && size(val) != sz
@@ -465,7 +472,7 @@ function validate_parameter_type(ic::IndexCache, stype, sz, sym, index, val)
         # This is for duals and other complicated number types
         etype = SciMLBase.parameterless_type(etype)
         eltype(val) <: etype || throw(ParameterTypeException(
-            :validate_parameter_type, sym, AbstractArray{etype}, val))
+            :validate_parameter_type, sym === nothing ? index : sym, AbstractArray{etype}, val))
     else
         # Real check
         if stype <: Real
@@ -473,7 +480,8 @@ function validate_parameter_type(ic::IndexCache, stype, sz, sym, index, val)
         end
         stype = SciMLBase.parameterless_type(stype)
         val isa stype ||
-            throw(ParameterTypeException(:validate_parameter_type, sym, stype, val))
+            throw(ParameterTypeException(
+                :validate_parameter_type, sym === nothing ? index : sym, stype, val))
     end
 end
 
@@ -485,6 +493,9 @@ function indp_to_system(indp)
 end
 
 function SymbolicIndexingInterface.remake_buffer(indp, oldbuf::MTKParameters, idxs, vals)
+    _remake_buffer(indp, oldbuf, idxs, vals)
+end
+function _remake_buffer(indp, oldbuf::MTKParameters, idxs, vals; validate = true)
     newbuf = @set oldbuf.tunable = similar(oldbuf.tunable, Any)
     @set! newbuf.discrete = Tuple(similar(buf, Any) for buf in newbuf.discrete)
     @set! newbuf.constant = Tuple(similar(buf, Any) for buf in newbuf.constant)
diff --git a/test/extensions/Project.toml b/test/extensions/Project.toml
index d8d3d64605..81097d98d2 100644
--- a/test/extensions/Project.toml
+++ b/test/extensions/Project.toml
@@ -1,5 +1,7 @@
 [deps]
 BifurcationKit = "0f109fa4-8a5d-4b75-95aa-f515264e7665"
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
diff --git a/test/extensions/ad.jl b/test/extensions/ad.jl
index 1946db5277..954b868a1e 100644
--- a/test/extensions/ad.jl
+++ b/test/extensions/ad.jl
@@ -6,6 +6,9 @@ using SciMLStructures
 using OrdinaryDiffEq
 using SciMLSensitivity
 using ForwardDiff
+using ChainRulesCore
+using ChainRulesCore: NoTangent
+using ChainRulesTestUtils: test_rrule, rand_tangent
 
 @variables x(t)[1:3] y(t)
 @parameters p[1:3, 1:3] q
@@ -51,3 +54,52 @@ end
 
     @test ForwardDiff.gradient(x_at_0, [0.3, 0.7]) == zeros(2)
 end
+
+@parameters a b[1:3] c(t) d::Integer e[1:3] f[1:3, 1:3]::Int g::Vector{AbstractFloat} h::String
+@named sys = ODESystem(
+    Equation[], t, [], [a, b, c, d, e, f, g, h],
+    continuous_events = [[a ~ 0] => [c ~ 0]])
+sys = complete(sys)
+
+ivs = Dict(c => 3a, b => ones(3), a => 1.0, d => 4, e => [5.0, 6.0, 7.0],
+    f => ones(Int, 3, 3), g => [0.1, 0.2, 0.3], h => "foo")
+
+ps = MTKParameters(sys, ivs)
+
+varmap = Dict(a => 1.0f0, b => 3ones(Float32, 3), c => 2.0,
+    e => Float32[0.4, 0.5, 0.6], g => ones(Float32, 4))
+get_values = getp(sys, [a, b..., c, e...])
+get_g = getp(sys, g)
+for (_idxs, vals) in [
+    # all portions
+    (collect(keys(varmap)), collect(values(varmap))),
+    # non-arrays
+    (keys(varmap), values(varmap)),
+    # tunable only
+    ([a], [varmap[a]]),
+    ([a, b], (varmap[a], varmap[b])),
+    ([a, b[2]], (varmap[a], varmap[b][2]))
+]
+    for idxs in [_idxs, map(i -> parameter_index(sys, i), collect(_idxs))]
+        loss = function (p)
+            newps = remake_buffer(sys, ps, idxs, p)
+            return sum(get_values(newps)) + sum(get_g(newps))
+        end
+
+        grad = Zygote.gradient(loss, vals)[1]
+        for (val, g) in zip(vals, grad)
+            @test eltype(val) == eltype(g)
+            if val isa Number
+                @test isone(g)
+            else
+                @test all(isone, g)
+            end
+        end
+    end
+end
+
+idxs = (parameter_index(sys, a), parameter_index(sys, b))
+vals = (1.0f0, 3ones(Float32, 3))
+tangent = rand_tangent(ps)
+fwd, back = ChainRulesCore.rrule(remake_buffer, sys, ps, idxs, vals)
+@inferred back(tangent)