diff --git a/Project.toml b/Project.toml
index efc4a6c..6b542ee 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "BlockSparseArrays"
 uuid = "2c9a651f-6452-4ace-a6ac-809f4280fbb4"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.7.19"
+version = "0.7.20"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/BlockArraysExtensions/blockedunitrange.jl b/src/BlockArraysExtensions/blockedunitrange.jl
index 3577905..0856238 100644
--- a/src/BlockArraysExtensions/blockedunitrange.jl
+++ b/src/BlockArraysExtensions/blockedunitrange.jl
@@ -216,22 +216,111 @@ function to_blockindices(a::AbstractBlockedUnitRange{<:Integer}, I::UnitRange{<:
   )
 end
 
-struct BlockIndexVector{T<:Integer,I<:AbstractVector{T},TB<:Integer} <:
-       AbstractVector{BlockIndex{1,Tuple{TB},Tuple{T}}}
-  block::Block{1,TB}
+struct GenericBlockIndex{N,TI<:Tuple{Vararg{Integer,N}},Tα<:Tuple{Vararg{Any,N}}}
+  I::TI
+  α::Tα
+end
+@inline function GenericBlockIndex(a::NTuple{N,Block{1}}, b::Tuple) where {N}
+  return GenericBlockIndex(Int.(a), b)
+end
+@inline function GenericBlockIndex(::Tuple{}, b::Tuple{})
+  return GenericBlockIndex{0,Tuple{},Tuple{}}((), ())
+end
+@inline GenericBlockIndex(a::Integer, b) = GenericBlockIndex((a,), (b,))
+@inline GenericBlockIndex(a::Tuple, b) = GenericBlockIndex(a, (b,))
+@inline GenericBlockIndex(a::Integer, b::Tuple) = GenericBlockIndex((a,), b)
+@inline GenericBlockIndex() = GenericBlockIndex((), ())
+@inline GenericBlockIndex(a::Block, b::Tuple) = GenericBlockIndex(a.n, b)
+@inline GenericBlockIndex(a::Block, b) = GenericBlockIndex(a, (b,))
+@inline function GenericBlockIndex(
+  I::Tuple{Vararg{Integer,N}}, α::Tuple{Vararg{Any,M}}
+) where {M,N}
+  M <= N || throw(ArgumentError("number of indices must not exceed the number of blocks"))
+  α2 = ntuple(k -> k <= M ? α[k] : 1, N)
+  GenericBlockIndex(I, α2)
+end
+BlockArrays.block(b::GenericBlockIndex) = Block(b.I...)
+BlockArrays.blockindex(b::GenericBlockIndex{1}) = b.α[1]
+function GenericBlockIndex(indcs::Tuple{Vararg{GenericBlockIndex{1},N}}) where {N}
+  GenericBlockIndex(block.(indcs), blockindex.(indcs))
+end
+function print_tuple_elements(io::IO, @nospecialize(t))
+  if !isempty(t)
+    print(io, t[1])
+    for n in t[2:end]
+      print(io, ", ", n)
+    end
+  end
+  return nothing
+end
+function Base.show(io::IO, B::GenericBlockIndex)
+  show(io, Block(B.I...))
+  print(io, "[")
+  print_tuple_elements(io, B.α)
+  print(io, "]")
+  return nothing
+end
+
+using Base: @propagate_inbounds
+@propagate_inbounds function Base.getindex(b::AbstractVector, K::GenericBlockIndex{1})
+  return b[Block(K.I[1])][K.α[1]]
+end
+@propagate_inbounds function Base.getindex(
+  b::AbstractArray{T,N}, K::GenericBlockIndex{N}
+) where {T,N}
+  return b[block(K)][K.α...]
+end
+@propagate_inbounds function Base.getindex(
+  b::AbstractArray, K::GenericBlockIndex{1}, J::GenericBlockIndex{1}...
+)
+  return b[GenericBlockIndex(tuple(K, J...))]
+end
+
+function blockindextype(TB::Type{<:Integer}, TI::Vararg{Type{<:Integer},N}) where {N}
+  return BlockIndex{N,NTuple{N,TB},Tuple{TI...}}
+end
+function blockindextype(TB::Type{<:Integer}, TI::Vararg{Type,N}) where {N}
+  return GenericBlockIndex{N,NTuple{N,TB},Tuple{TI...}}
+end
+
+struct BlockIndexVector{N,I<:NTuple{N,AbstractVector},TB<:Integer,BT} <: AbstractArray{BT,N}
+  block::Block{N,TB}
   indices::I
+  function BlockIndexVector(
+    block::Block{N,TB}, indices::I
+  ) where {N,I<:NTuple{N,AbstractVector},TB<:Integer}
+    BT = blockindextype(TB, eltype.(indices)...)
+    return new{N,I,TB,BT}(block, indices)
+  end
+end
+function BlockIndexVector(block::Block{1}, indices::AbstractVector)
+  return BlockIndexVector(block, (indices,))
+end
+Base.size(a::BlockIndexVector) = length.(a.indices)
+function Base.getindex(a::BlockIndexVector{N}, I::Vararg{Integer,N}) where {N}
+  return a.block[map((r, i) -> r[i], a.indices, I)...]
 end
-Base.length(a::BlockIndexVector) = length(a.indices)
-Base.size(a::BlockIndexVector) = (length(a),)
-BlockArrays.Block(a::BlockIndexVector) = a.block
-Base.getindex(a::BlockIndexVector, I::Integer) = Block(a)[a.indices[I]]
-Base.copy(a::BlockIndexVector) = BlockIndexVector(a.block, copy(a.indices))
+BlockArrays.block(b::BlockIndexVector) = b.block
+BlockArrays.Block(b::BlockIndexVector) = b.block
+
+Base.copy(a::BlockIndexVector) = BlockIndexVector(a.block, copy.(a.indices))
+
+using ArrayLayouts: LayoutArray
+@propagate_inbounds Base.getindex(b::AbstractArray{T,N}, K::BlockIndexVector{N}) where {T,N} = b[block(
+  K
+)][K.indices...]
+@propagate_inbounds Base.getindex(b::LayoutArray{T,N}, K::BlockIndexVector{N}) where {T,N} = b[block(
+  K
+)][K.indices...]
+@propagate_inbounds Base.getindex(b::LayoutArray{T,1}, K::BlockIndexVector{1}) where {T} = b[block(
+  K
+)][K.indices...]
 
 function to_blockindices(a::AbstractBlockedUnitRange{<:Integer}, I::AbstractArray{Bool})
   I_blocks = blocks(BlockedVector(I, blocklengths(a)))
   I′_blocks = map(eachindex(I_blocks)) do b
     I_b = findall(I_blocks[b])
-    BlockIndexVector(Block(b), I_b)
+    return BlockIndexVector(Block(b), I_b)
   end
   return mortar(filter(!isempty, I′_blocks))
 end
diff --git a/src/abstractblocksparsearray/views.jl b/src/abstractblocksparsearray/views.jl
index 4a40947..1bfe48f 100644
--- a/src/abstractblocksparsearray/views.jl
+++ b/src/abstractblocksparsearray/views.jl
@@ -95,7 +95,7 @@ to_block(I::BlockIndexRange{1}) = Block(I)
 to_block(I::BlockIndexVector) = Block(I)
 to_block_indices(I::Block{1}) = Colon()
 to_block_indices(I::BlockIndexRange{1}) = only(I.indices)
-to_block_indices(I::BlockIndexVector) = I.indices
+to_block_indices(I::BlockIndexVector) = only(I.indices)
 
 function Base.view(
   a::AbstractBlockSparseArray{<:Any,N},