The history of generalized “stacked bases” theorem origins from the result of Hill and Megibben on abelian groups. We extend this theorem for modules over semiperfect rings and as a consequence we show that for a submodule H of a projective module G over a semiperfect ring, the following conditions are equivalent: there exists a decomposition (Formula presented.) into a direct sum of indecomposable modules P_i, such that (Formula presented.) G/H is a direct sum of a family of modules, isomorphic to factor modules of principal indecomposable modules.