Polish numerals and negation participate in case alternations, a phenomenon in which their ability to trigger genitive case assignment is determined by the case environment of the nominal. In particular, oblique case contexts appear to block the genitive of numerals and negation. This phenomenon is often contextualized within the structural-inherent case distinction (Chomsky 1981, 1986; Babby 1987), with the case type (structural, inherent) playing a primary role in determining case realization; a common assumption is that only a single case is assigned per nominal. This paper proposes an alternative analysis, which takes case stacking to be freely available in the syntax. A post-syntactic algorithm then determines the final choice of overt case in contexts of case competitions. This paper further shows that certain cases appear to have a lexical requirement, leading to case percolation in the context of numerals, which are argued to be semi-lexical. Together, these assumptions accurately model the case alternations of numerals and negation, and furthermore, tell us something about the nature of case.