diff --git a/Project.toml b/Project.toml
index f61a4c4..0398304 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,10 +11,15 @@ MutableArithmetics = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+StarAlgebras = "0c0c59c1-dc5f-42e9-9a8b-b5dc384a6cd1"
 
 [compat]
 MacroTools = "0.5"
 MultivariatePolynomials = "0.5.8"
 MutableArithmetics = "1"
 Reexport = "1"
+StarAlgebras = "0.3"
 julia = "1.10"
+
+[sources]
+MultivariatePolynomials = {url = "https://github.com/JuliaAlgebra/MultivariatePolynomials.jl.git", rev = "claude/implement-promote-basis-0gQqp"}
diff --git a/src/TypedPolynomials.jl b/src/TypedPolynomials.jl
index 79eb06e..a7706fe 100644
--- a/src/TypedPolynomials.jl
+++ b/src/TypedPolynomials.jl
@@ -36,5 +36,6 @@ include("conversion.jl")
 include("promotion.jl")
 include("call.jl")
 include("macros.jl")
+include("sa.jl")
 
 end # module
diff --git a/src/sa.jl b/src/sa.jl
new file mode 100644
index 0000000..8dcdb96
--- /dev/null
+++ b/src/sa.jl
@@ -0,0 +1,21 @@
+import StarAlgebras as SA
+
+function SA.promote_with_map(
+    m::Monomial{V,N},
+    all_vars::Tuple{Vararg{Variable}},
+    map::MP.ExponentMap,
+) where {V,N}
+    new_exps = map(m.exponents)
+    M = length(all_vars)
+    new_mono = Monomial{all_vars,M}(new_exps)
+    return new_mono, map
+end
+
+function SA.promote_with_map(
+    v::Variable,
+    all_vars::Tuple{Vararg{Variable}},
+    map::MP.ExponentMap,
+)
+    return SA.promote_with_map(Monomial(v), all_vars, map)
+end
+