diff --git a/docs/src/Changelog.md b/docs/src/Changelog.md
index 6fd79f4df..2f5e568f2 100644
--- a/docs/src/Changelog.md
+++ b/docs/src/Changelog.md
@@ -22,6 +22,7 @@ When releasing a new version, move the "Unreleased" changes to a new version sec
 
 ### Added
 
+- A more robust promotion system for `storagetype`s to better handle working with unions and other abstract tensor map types ([#370](https://github.com/QuantumKitHub/TensorKit.jl/pull/370)).
 
 ### Changed
 
diff --git a/src/tensors/abstracttensor.jl b/src/tensors/abstracttensor.jl
index 7f068369a..2d7239460 100644
--- a/src/tensors/abstracttensor.jl
+++ b/src/tensors/abstracttensor.jl
@@ -38,12 +38,30 @@ function InnerProductStyle(::Type{TT}) where {TT <: AbstractTensorMap}
     return InnerProductStyle(spacetype(TT))
 end
 
+# storage types and promotion system
+# ----------------------------------
 @doc """
     storagetype(t::AbstractTensorMap) -> Type{A<:AbstractVector}
     storagetype(T::Type{<:AbstractTensorMap}) -> Type{A<:AbstractVector}
 
 Return the type of vector that stores the data of a tensor.
+If this is not overloaded for a given tensor type, the default value of `storagetype(scalartype(t))` is returned.
+
+See also [`similarstoragetype`](@ref).
 """ storagetype
+storagetype(t) = storagetype(typeof(t))
+function storagetype(::Type{T}) where {T <: AbstractTensorMap}
+    if T isa Union
+        # attempt to be slightly more specific by promoting unions
+        Ma = storagetype(T.a)
+        Mb = storagetype(T.b)
+        return promote_storagetype(Ma, Mb)
+    else
+        # fallback definition by using scalartype
+        return similarstoragetype(scalartype(T))
+    end
+end
+storagetype(T::Type) = throw(MethodError(storagetype, T))
 
 # storage type determination and promotion - hooks for specializing
 # the default implementation tries to leverarge inference and `similar`
@@ -69,6 +87,8 @@ appropriate storage types. Additionally this registers the default storage type
     used in constructor-like calls, and therefore will return the exact same type for a `DenseVector`
     input. The latter is used in `similar`-like calls, and therefore will return the type of calling
     `similar` on the given `DenseVector`, which need not coincide with the original type.
+
+See also [`promote_storagetype`](@ref).
 """ similarstoragetype
 
 # implement in type domain
@@ -102,6 +122,74 @@ similarstoragetype(::Type{D}, ::Type{T}) where {D <: AbstractDict{<:Sector, <:Ab
 # default storage type for numbers
 similarstoragetype(::Type{T}) where {T <: Number} = Vector{T}
 
+@doc """
+    promote_storagetype([T], A, B, C...)
+    promote_storagetype([T], TA, TB, TC...)
+
+Determine an appropriate storage type for the combination of tensors `A` and `B`, or tensors of type `TA` and `TB`.
+Optionally, a scalartype `T` for the destination can be supplied that might differ from the inputs.
+""" promote_storagetype
+
+@inline promote_storagetype(A::AbstractTensorMap, B::AbstractTensorMap, Cs::AbstractTensorMap...) =
+    promote_storagetype(storagetype(A), storagetype(B), map(storagetype, Cs)...)
+@inline promote_storagetype(::Type{T}, A::AbstractTensorMap, B::AbstractTensorMap, Cs::AbstractTensorMap...) where {T <: Number} =
+    promote_storagetype(similarstoragetype(A, T), similarstoragetype(B, T), map(Base.Fix2(similarstoragetype, T), Cs)...)
+
+@inline function promote_storagetype(
+        ::Type{A}, ::Type{B}, Cs::Type{<:AbstractTensorMap}...
+    ) where {A <: AbstractTensorMap, B <: AbstractTensorMap}
+    return promote_storagetype(storagetype(A), storagetype(B), map(storagetype, Cs)...)
+end
+@inline function promote_storagetype(
+        ::Type{T}, ::Type{A}, ::Type{B}, Cs::Type{<:AbstractTensorMap}...
+    ) where {T <: Number, A <: AbstractTensorMap, B <: AbstractTensorMap}
+    return promote_storagetype(similarstoragetype(A, T), similarstoragetype(B, T), map(Base.Fix2(similarstoragetype, T), Cs)...)
+end
+
+# promotion system in the same spirit as base/promotion.jl
+promote_storagetype(::Type{Base.Bottom}, ::Type{Base.Bottom}) = Base.Bottom
+promote_storagetype(::Type{T}, ::Type{T}) where {T} = T
+promote_storagetype(::Type{T}, ::Type{Base.Bottom}) where {T} = T
+promote_storagetype(::Type{Base.Bottom}, ::Type{T}) where {T} = T
+
+function promote_storagetype(::Type{T}, ::Type{S}) where {T, S}
+    @inline
+    # Try promote_storage_rule in both orders. Typically only one is defined,
+    # and there is a fallback returning Bottom below, so the common case is
+    #   promote_storagetype(T, S) =>
+    #   promote_storage_result(T, S, result, Bottom) =>
+    #   typejoin(result, Bottom) => result
+    return promote_storage_result(T, S, promote_storage_rule(T, S), promote_storage_rule(S, T))
+end
+
+@inline promote_storagetype(T, S, U) = promote_storagetype(promote_storagetype(T, S), U)
+@inline promote_storagetype(T, S, U, V...) = promote_storagetype(promote_storagetype(T, S), U, V...)
+
+@doc """
+    promote_storage_rule(type1, type2)
+
+Specifies what type should be used by [`promote_storagetype`](@ref) when given values of types `type1` and
+`type2`. This function should not be called directly, but should have definitions added to
+it for new types as appropriate.
+""" promote_storage_rule
+
+promote_storage_rule(::Type, ::Type) = Base.Bottom
+# Define some methods to avoid needing to enumerate unrelated possibilities when presented
+# with Type{<:T}, and return a value in general accordance with the result given by promote_type
+promote_storage_rule(::Type{Base.Bottom}, slurp...) = Base.Bottom
+promote_storage_rule(::Type{Base.Bottom}, ::Type{Base.Bottom}, slurp...) = Base.Bottom # not strictly necessary, since the next method would match unambiguously anyways
+promote_storage_rule(::Type{Base.Bottom}, ::Type{T}, slurp...) where {T} = T
+promote_storage_rule(::Type{T}, ::Type{Base.Bottom}, slurp...) where {T} = T
+
+promote_storage_result(::Type, ::Type, ::Type{T}, ::Type{S}) where {T, S} = (@inline; promote_storagetype(T, S))
+# If no promote_storage_rule is defined, both directions give Bottom => error
+promote_storage_result(T::Type, S::Type, ::Type{Base.Bottom}, ::Type{Base.Bottom}) =
+    throw(ArgumentError("No promotion rule defined for storagetype `$T` and `$S`"))
+
+# promotion rules for common vector types
+promote_storage_rule(::Type{T}, ::Type{S}) where {T <: DenseVector, S <: DenseVector} =
+    T === S ? T : throw(ArgumentError("No promotion rule defined for storagetype `$T` and `$S`"))
+
 # tensor characteristics: space and index information
 #-----------------------------------------------------
 """
@@ -224,8 +312,7 @@ end
 # tensor characteristics: work on instances and pass to type
 #------------------------------------------------------------
 InnerProductStyle(t::AbstractTensorMap) = InnerProductStyle(typeof(t))
-storagetype(t) = storagetype(typeof(t))
-storagetype(T::Type) = throw(MethodError(storagetype, T))
+
 blocktype(t::AbstractTensorMap) = blocktype(typeof(t))
 
 numout(t::AbstractTensorMap) = numout(typeof(t))
diff --git a/src/tensors/braidingtensor.jl b/src/tensors/braidingtensor.jl
index 9c92c67a1..97fb2fbba 100644
--- a/src/tensors/braidingtensor.jl
+++ b/src/tensors/braidingtensor.jl
@@ -57,9 +57,17 @@ end
 
 space(b::BraidingTensor) = b.adjoint ? b.V1 ⊗ b.V2 ← b.V2 ⊗ b.V1 : b.V2 ⊗ b.V1 ← b.V1 ⊗ b.V2
 
-# TODO: this will probably give issues with GPUs, so we should try to avoid
-# calling this method alltogether
-storagetype(::Type{BraidingTensor{T, S}}) where {T, S} = Vector{T}
+# specializations to ignore the storagetype of BraidingTensor
+promote_storagetype(::Type{A}, ::Type{B}) where {A <: BraidingTensor, B <: AbstractTensorMap} = storagetype(B)
+promote_storagetype(::Type{A}, ::Type{B}) where {A <: AbstractTensorMap, B <: BraidingTensor} = storagetype(A)
+promote_storagetype(::Type{A}, ::Type{B}) where {A <: BraidingTensor, B <: BraidingTensor} = storagetype(A)
+
+promote_storagetype(::Type{T}, ::Type{A}, ::Type{B}) where {T <: Number, A <: BraidingTensor, B <: AbstractTensorMap} =
+    similarstoragetype(B, T)
+promote_storagetype(::Type{T}, ::Type{A}, ::Type{B}) where {T <: Number, A <: AbstractTensorMap, B <: BraidingTensor} =
+    similarstoragetype(A, T)
+promote_storagetype(::Type{T}, ::Type{A}, ::Type{B}) where {T <: Number, A <: BraidingTensor, B <: BraidingTensor} =
+    similarstoragetype(A, T)
 
 function Base.getindex(b::BraidingTensor)
     sectortype(b) === Trivial || throw(SectorMismatch())
diff --git a/src/tensors/diagonal.jl b/src/tensors/diagonal.jl
index 8232710c5..7652a2fba 100644
--- a/src/tensors/diagonal.jl
+++ b/src/tensors/diagonal.jl
@@ -272,9 +272,8 @@ function TO.tensorcontract_type(
         ::Index2Tuple{1, 1}
     )
     S = check_spacetype(A, B)
-    TC′ = promote_permute(TC, sectortype(S))
-    M = promote_storagetype(similarstoragetype(A, TC′), similarstoragetype(B, TC′))
-    return DiagonalTensorMap{TC, S, M}
+    M = promote_storagetype(promote_permute(TC, sectortype(S)), A, B)
+    return DiagonalTensorMap{scalartype(M), S, M}
 end
 
 function TO.tensoralloc(
@@ -303,9 +302,8 @@ end
 
 function compose_dest(A::DiagonalTensorMap, B::DiagonalTensorMap)
     S = check_spacetype(A, B)
-    TC = TO.promote_contract(scalartype(A), scalartype(B), One)
-    M = promote_storagetype(similarstoragetype(A, TC), similarstoragetype(B, TC))
-    TTC = DiagonalTensorMap{TC, S, M}
+    M = promote_storagetype(TO.promote_contract(scalartype(A), scalartype(B), One), A, B)
+    TTC = DiagonalTensorMap{scalartype(M), S, M}
     structure = codomain(A) ← domain(B)
     return TO.tensoralloc(TTC, structure, Val(false))
 end
diff --git a/src/tensors/linalg.jl b/src/tensors/linalg.jl
index 5ac948802..900ee84fe 100644
--- a/src/tensors/linalg.jl
+++ b/src/tensors/linalg.jl
@@ -23,8 +23,7 @@ LinearAlgebra.normalize(t::AbstractTensorMap, p::Real = 2) = scale(t, inv(norm(t
 # permutations, which might require complex scalartypes even if the inputs are real.
 function compose_dest(A::AbstractTensorMap, B::AbstractTensorMap)
     S = check_spacetype(A, B)
-    TC = TO.promote_contract(scalartype(A), scalartype(B), One)
-    M = promote_storagetype(similarstoragetype(A, TC), similarstoragetype(B, TC))
+    M = promote_storagetype(TO.promote_contract(scalartype(A), scalartype(B), One), A, B)
     TTC = tensormaptype(S, numout(A), numin(B), M)
     structure = codomain(A) ← domain(B)
     return TO.tensoralloc(TTC, structure, Val(false))
diff --git a/src/tensors/tensor.jl b/src/tensors/tensor.jl
index 12281d758..615c67775 100644
--- a/src/tensors/tensor.jl
+++ b/src/tensors/tensor.jl
@@ -560,7 +560,6 @@ end
 function Base.promote_rule(
         ::Type{<:TT₁}, ::Type{<:TT₂}
     ) where {S, N₁, N₂, TT₁ <: TensorMap{<:Any, S, N₁, N₂}, TT₂ <: TensorMap{<:Any, S, N₁, N₂}}
-    T = VectorInterface.promote_add(scalartype(TT₁), scalartype(TT₂))
-    A = promote_storagetype(similarstoragetype(TT₁, T), similarstoragetype(TT₂, T))
+    A = promote_storagetype(VectorInterface.promote_add(scalartype(TT₁), scalartype(TT₂)), TT₁, TT₂)
     return tensormaptype(S, N₁, N₂, A)
 end
diff --git a/src/tensors/tensoroperations.jl b/src/tensors/tensoroperations.jl
index 81894d140..0820fe1af 100644
--- a/src/tensors/tensoroperations.jl
+++ b/src/tensors/tensoroperations.jl
@@ -153,16 +153,10 @@ function TO.tensorcontract_type(
         ::Index2Tuple{N₁, N₂}
     ) where {N₁, N₂}
     S = check_spacetype(A, B)
-    TC′ = promote_permute(TC, sectortype(S))
-    M = promote_storagetype(similarstoragetype(A, TC′), similarstoragetype(B, TC′))
+    M = promote_storagetype(promote_permute(TC, sectortype(S)), A, B)
     return tensormaptype(S, N₁, N₂, M)
 end
 
-# TODO: handle actual promotion rule system
-function promote_storagetype(::Type{M₁}, ::Type{M₂}) where {M₁, M₂}
-    return M₁ === M₂ ? M₁ : throw(ArgumentError("Cannot determine storage type for combining `$M₁` and `$M₂`"))
-end
-
 function TO.tensorcontract_structure(
         A::AbstractTensorMap, pA::Index2Tuple, conjA::Bool,
         B::AbstractTensorMap, pB::Index2Tuple, conjB::Bool,