In this article, we study modules with the weak $FI$-extending property. We prove that if $M$ satisfies weak $FI$-extending, pseudo duo, $C_3$ properties and $M/\mathrm{Soc}M$ has finite uniform dimension then $M$ decomposes into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if $M$ satisfies the weak $FI$-extending, pseudo duo, $C_3$ properties and ascending (or descending) chain condition on essential submodules then $M=M_1\oplus M_2$ for some semisimple submodule $M_1$ and Noetherian (or Artinian, respectively)...