The aim of this article is to briefly analyze the agreement patterns in Polish constructions with quantified subjects and adjectival predicates/participles, and propose an account built on the nanosyntactic ideas regarding the nature of case, i.e., split Kase Phrase (Caha 2009, 2010). In the analysis we address the troublesome issues regarding the Genitive of Quantification, i.e., the source of Genitive on the nominal complement in structural contexts, and the optionality in agreement in case between the adjectival predicate/participle and the numeral (≥5), or the noun of the quantified subject. The essential part of our proposal is based on the articulated Kase Phrase in the functional sequence of the extended nominal projection and its ro...