This work introduces and investigates a generalization of extending semimodules via weak-supplement subsemimodules. An S-semimodule L is called weakly-supplement extending (shortly, 𝓌𝓈e—semimodule) if every subsemimodule of L is essential in a weakly-supplement subsemimodule of L. We asserted that the class of 𝓌𝓈e-semimodules properly contains both extending and lifting semimodules. Analogously to extending semimodules, this paper gives many characterizations of 𝓌𝓈e-semimodules. We showed that L is wse-semimodule if and only if each closed subsemimodule of L is a weakly supplement subsemimodule of L. Moreover, we discussed the relation of wse-semimodule and its relation with other known classes of semimodule, such as ⨁-supplemented, lifting, and uniform semimodules. We inspected whether the 𝓌𝓈e-semimodule property is satisfied under direct sum, subsemimodule, epimorphic image, and inverse image.