diff --git a/src/sparse_coeffs.jl b/src/sparse_coeffs.jl
index 1a4300d..3e7236f 100644
--- a/src/sparse_coeffs.jl
+++ b/src/sparse_coeffs.jl
@@ -13,8 +13,17 @@ function Base.copy(sc::SparseCoefficients)
     return SparseCoefficients(copy(keys(sc)), copy(values(sc)))
 end
 
+function _search(keys::Tuple, key)
+    # `searchsortedfirst` is not defined for `Tuple`
+    return findfirst(isequal(key), keys)
+end
+
+function _search(keys, key::K) where {K}
+    return searchsortedfirst(keys, key; lt = comparable(K))
+end
+
 function Base.getindex(sc::SparseCoefficients{K}, key::K) where {K}
-    k = searchsortedfirst(sc.basis_elements, key; lt = comparable(K))
+    k = _search(sc.basis_elements, key)
     if k in eachindex(sc.basis_elements)
         v = sc.values[k]
         if sc.basis_elements[k] == key
@@ -30,7 +39,7 @@ end
 function Base.setindex!(sc::SparseCoefficients{K}, val, key::K) where {K}
     k = searchsortedfirst(sc.basis_elements, key; lt = comparable(K))
     if k in eachindex(sc.basis_elements) && sc.basis_elements[k] == key
-        sc.values[k] += val
+        sc.values[k] = val
     else
         insert!(sc.basis_elements, k, key)
         insert!(sc.values, k, val)
@@ -38,6 +47,55 @@ function Base.setindex!(sc::SparseCoefficients{K}, val, key::K) where {K}
     return sc
 end
 
+################
+# Broadcasting #
+################
+
+struct BroadcastStyle{K} <: Broadcast.BroadcastStyle end
+
+Base.broadcastable(sc::SparseCoefficients) = sc
+Base.BroadcastStyle(::Type{<:SparseCoefficients{K}}) where {K} = BroadcastStyle{K}()
+# Disallow mixing broadcasts.
+function Base.BroadcastStyle(::BroadcastStyle, ::Base.BroadcastStyle)
+    return throw(
+        ArgumentError(
+            "Cannot broadcast `StarAlgebras.SparseCoefficients` with" *
+            " another array of different type",
+        ),
+    )
+end
+
+# Allow broadcasting over scalars.
+function Base.BroadcastStyle(style::BroadcastStyle, ::Base.Broadcast.DefaultArrayStyle{0})
+    return style
+end
+
+# Used for broadcasting
+Base.axes(sc::SparseCoefficients) = (sc.basis_elements,)
+#Base.Broadcast.BroadcastStyle(::Type{<:SparseCoefficients{K}}) where {K} = SparseArrays.HigherOrderFns.SparseVecStyle()
+#SparseArrays.HigherOrderFns.nonscalararg(::SparseCoefficients) = true
+
+# `_get_arg` and `getindex` are inspired from `JuMP.Containers.SparseAxisArray`
+_getindex(x::SparseCoefficients, index) = getindex(x, index)
+_getindex(x::Any, ::Any) = x
+_getindex(x::Ref, ::Any) = x[]
+
+function _get_arg(args::Tuple, index)
+    return (_getindex(first(args), index), _get_arg(Base.tail(args), index)...)
+end
+_get_arg(::Tuple{}, _) = ()
+
+function Base.getindex(bc::Broadcast.Broadcasted{<:BroadcastStyle}, index)
+    return bc.f(_get_arg(bc.args, index)...)
+end
+
+function Base.similar(bc::Broadcast.Broadcasted{<:BroadcastStyle}, ::Type{T}) where {T}
+    return similar(_first_sparse_coeffs(bc.args...), T)
+end
+
+_first_sparse_coeffs(c::SparseCoefficients, args...) = c
+_first_sparse_coeffs(_, args...) = _first_sparse_coeffs(args...)
+
 function Base.zero(sc::SparseCoefficients)
     return SparseCoefficients(empty(keys(sc)), empty(values(sc)))
 end
@@ -55,7 +113,7 @@ function similar_type(::Type{SparseCoefficients{K,V,Vk,Vv}}, ::Type{T}) where {K
 end
 
 function Base.similar(s::SparseCoefficients, ::Type{T} = valtype(s)) where {T}
-    return SparseCoefficients(_similar(s.basis_elements), _similar(s.values, T))
+    return SparseCoefficients(collect(s.basis_elements), _similar(s.values, T))
 end
 
 function MA.mutability(
diff --git a/test/caching_allocations.jl b/test/caching_allocations.jl
index 30a4b4a..862ec22 100644
--- a/test/caching_allocations.jl
+++ b/test/caching_allocations.jl
@@ -100,4 +100,16 @@ end
     @test _test_op(+, Z, Y) == _test_op(+, Y, Y)
     @test _test_op(-, Z, Z) == _test_op(*, 0, Z)
     @test _test_op(-, Z, Z) == _test_op(-, Y, Z)
+
+    for X in [Y, Z]
+        c = coeffs(X)
+        res = 2 .* c
+        @test c .* 2 == res
+        @test c .+ 1 == res
+        @test 1 .+ c == res
+        @test MA.Zero() .+ c == c
+        @test c .+ MA.Zero() == c
+        err = ArgumentError("Cannot broadcast `StarAlgebras.SparseCoefficients` with another array of different type")
+        @test_throws err c .+ ones(3)
+    end
 end