A generalization of $\oplus$-cofinitely supplemented modules

‎We say that a module $M$ is a \emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{ʹ}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{ʹ}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $\oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove that a $\pi$-projective module $M$ is a cms-module if and only if $M$ is $\oplus$-cofinitely supplemented‎. ‎Finally‎, ‎we show that every free $R$-module is a cms-module if and only if $R$ is semiperfect.