The aim of this paper is investigating the existence of one or more weak solutions of the coupled quasilinear elliptic system of gradient type where is an open bounded domain, , and , are -Carathéodory functions on with partial derivatives , respectively , while , are given Carathéodory maps defined on which are partial derivatives of a function . We prove that, even if the coefficients make the variational approach more difficult, under suitable hypotheses functional , related to problem (P), admits at least one critical point in the “right” Banach space . Moreover, if is even, then (P) has infinitely many weak bounded solutions. The proof, which exploits the interaction between two different norms, is based on a weak version of the Cerami–Palais–Smale condition, a “good” decomposition of the Banach space and suitable generalizations of the Ambrosetti–Rabinowitz Mountain Pass Theorems.