Let R be a commutative ring with identity and M a unital R-module. For any submodule N of M and non-empty subset T of R, let SMT (N)={m ∈ M : rm∈ N for some r ∈ R\T}. In this article we study conditions under which SMT  (N) is a submodule of M and investigate when it is a union of prime submodules.