diff --git a/Project.toml b/Project.toml
index 0488c683..77955591 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "RecursiveArrayTools"
 uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
-version = "4.0.1"
 authors = ["Chris Rackauckas <accounts@chrisrackauckas.com>"]
+version = "4.0.1"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
@@ -20,6 +20,7 @@ FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 MonteCarloMeasurements = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
 Polyester = "f517fe37-dbe3-4b94-8317-1923a5111588"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
@@ -38,6 +39,7 @@ RecursiveArrayToolsForwardDiffExt = "ForwardDiff"
 RecursiveArrayToolsKernelAbstractionsExt = "KernelAbstractions"
 RecursiveArrayToolsMeasurementsExt = "Measurements"
 RecursiveArrayToolsMonteCarloMeasurementsExt = "MonteCarloMeasurements"
+RecursiveArrayToolsMooncakeExt = "Mooncake"
 RecursiveArrayToolsReverseDiffExt = ["ReverseDiff", "Zygote"]
 RecursiveArrayToolsSparseArraysExt = ["SparseArrays"]
 RecursiveArrayToolsStatisticsExt = "Statistics"
@@ -59,6 +61,7 @@ KernelAbstractions = "0.9.36"
 LinearAlgebra = "1.10"
 Measurements = "2.11"
 MonteCarloMeasurements = "1.2"
+Mooncake = "0.5"
 NLsolve = "4.5"
 Pkg = "1"
 Polyester = "0.7.16"
@@ -86,6 +89,7 @@ FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 MonteCarloMeasurements = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
@@ -102,4 +106,4 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "FastBroadcast", "ForwardDiff", "KernelAbstractions", "Measurements", "NLsolve", "Pkg", "Polyester", "Random", "SafeTestsets", "SparseArrays", "StaticArrays", "Statistics", "StructArrays", "Tables", "Test", "Unitful", "Zygote"]
+test = ["Aqua", "FastBroadcast", "ForwardDiff", "KernelAbstractions", "Measurements", "Mooncake", "NLsolve", "Pkg", "Polyester", "Random", "SafeTestsets", "SparseArrays", "StaticArrays", "Statistics", "StructArrays", "Tables", "Test", "Unitful", "Zygote"]
diff --git a/ext/RecursiveArrayToolsMooncakeExt.jl b/ext/RecursiveArrayToolsMooncakeExt.jl
new file mode 100644
index 00000000..d74ce862
--- /dev/null
+++ b/ext/RecursiveArrayToolsMooncakeExt.jl
@@ -0,0 +1,44 @@
+module RecursiveArrayToolsMooncakeExt
+
+using RecursiveArrayTools
+using Mooncake
+
+# `ArrayPartition` cotangent handling for `@from_chainrules` /
+# `@from_rrule`-generated rules.
+#
+# When an upstream ChainRules-based adjoint (e.g. SciMLSensitivity's
+# `_concrete_solve_adjoint` for an ODE whose state is an `ArrayPartition`,
+# such as the one produced by `SecondOrderODEProblem`) returns a parameter
+# / state cotangent as an `ArrayPartition`, Mooncake's
+# `@from_chainrules`/`@from_rrule` accumulator looks for an
+# `increment_and_get_rdata!` method matching
+# `(FData{NamedTuple{(:x,), Tuple{Tuple{Vector, …}}}}, NoRData, ArrayPartition)`
+# — and there isn't one by default, so the call falls through to the
+# generic error path:
+#
+#     ArgumentError: The fdata type Mooncake.FData{@NamedTuple{x::Tuple{Vector{Float32}, Vector{Float32}}}},
+#     rdata type Mooncake.NoRData, and tangent type
+#     RecursiveArrayTools.ArrayPartition{Float32, Tuple{Vector{Float32}, Vector{Float32}}}
+#     combination is not supported with @from_chainrules or @from_rrule.
+#
+# Add the missing dispatch.  An `ArrayPartition`'s only field is `x::Tuple`
+# of inner arrays, so the FData layout is
+# `FData{@NamedTuple{x::Tuple{...}}}` and the inner tuple positions line up
+# with `t.x`.  Walk the tuple element-by-element and forward each leaf to
+# the existing `increment_and_get_rdata!` for the leaf's array type, which
+# does the actual in-place accumulation.
+function Mooncake.increment_and_get_rdata!(
+        f::Mooncake.FData{@NamedTuple{x::T}},
+        r::Mooncake.NoRData,
+        t::ArrayPartition{P, T},
+    ) where {P, T <: Tuple}
+    fxs = f.data[:x]
+    txs = t.x
+    @assert length(fxs) == length(txs)
+    for i in eachindex(fxs)
+        Mooncake.increment_and_get_rdata!(fxs[i], Mooncake.NoRData(), txs[i])
+    end
+    return Mooncake.NoRData()
+end
+
+end
diff --git a/test/mooncake.jl b/test/mooncake.jl
new file mode 100644
index 00000000..6a0ff28e
--- /dev/null
+++ b/test/mooncake.jl
@@ -0,0 +1,39 @@
+using RecursiveArrayTools, Mooncake, Test
+
+# Regression test for the `RecursiveArrayToolsMooncakeExt` dispatch that
+# lets Mooncake's `@from_chainrules`/`@from_rrule` accumulator handle an
+# `ArrayPartition` cotangent returned by an upstream ChainRule (e.g.
+# SciMLSensitivity's `_concrete_solve_adjoint` for a `SecondOrderODEProblem`).
+# Without the extension, the call below fell through to Mooncake's generic
+# error path:
+#
+#     ArgumentError: The fdata type Mooncake.FData{@NamedTuple{x::Tuple{Vector{Float64}, Vector{Float64}}}},
+#     rdata type Mooncake.NoRData, and tangent type
+#     RecursiveArrayTools.ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}
+#     combination is not supported with @from_chainrules or @from_rrule.
+
+@testset "ArrayPartition increment_and_get_rdata!" begin
+    @test Base.get_extension(RecursiveArrayTools, :RecursiveArrayToolsMooncakeExt) !==
+          nothing
+
+    # Tangent produced by an upstream ChainRule.
+    t = ArrayPartition([1.0, 2.0], [3.0, 4.0])
+    # Pre-existing FData that the method should accumulate into in place.
+    f = Mooncake.FData((x = ([10.0, 20.0], [30.0, 40.0]),))
+
+    r = Mooncake.increment_and_get_rdata!(f, Mooncake.NoRData(), t)
+
+    @test r === Mooncake.NoRData()
+    @test f.data.x[1] == [11.0, 22.0]
+    @test f.data.x[2] == [33.0, 44.0]
+
+    # Three-way partition with Float32 leaves — exercises the inner
+    # per-leaf dispatch on a different eltype and arity.
+    t32 = ArrayPartition(Float32[1, 2], Float32[3, 4, 5], Float32[6])
+    f32 = Mooncake.FData((x = (Float32[10, 20], Float32[30, 40, 50], Float32[60]),))
+    r32 = Mooncake.increment_and_get_rdata!(f32, Mooncake.NoRData(), t32)
+    @test r32 === Mooncake.NoRData()
+    @test f32.data.x[1] == Float32[11, 22]
+    @test f32.data.x[2] == Float32[33, 44, 55]
+    @test f32.data.x[3] == Float32[66]
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 7bdb76c8..b87c9aa6 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -46,6 +46,7 @@ end
         @time @safetestset "StaticArrays Tests" include("copy_static_array_test.jl")
         @time @safetestset "Linear Algebra Tests" include("linalg.jl")
         @time @safetestset "Adjoint Tests" include("adjoints.jl")
+        @time @safetestset "Mooncake Tests" include("mooncake.jl")
         @time @safetestset "Measurement Tests" include("measurements.jl")
     end