In this paper we introduce the new class of QTAG-modules namely ω1-(ω + n)-projective modules, which is an amalgamation of three important classes of modules: n-bounded modules, the direct sum of uniserial modules and the countably generated modules. This class is given many equivalent characterizations including being the smallest class containing the (ω + n)- projective modules that is closed with respect to ω1-bijective homomorphisms.