A module $M$ is said to satisfy the $EC_{11}$ condition if every ec-submodule of $M$ has a complement which is a direct summand. We show that for a multiplication module over a commutative ring the $EC_{11}$ and P-extending conditions are equivalent. It is shown that the $EC_{11}$ property is not inherited by direct summands. Moreover, we prove that if $M$ is an $EC_{11}$-module where $SocM$ is an ec-submodule, then it is a direct sum of a module with essential socle and a module with zero socle. An example is given to show that the reverse of the last result does not hold.

Keywords: Extending module, ec-closed submodule, P-extending module, $C_{11}$-module, Multiplication module