Polyvalent vaccines use a mixture of Ags representing distinct pathogen strains to induce an immune response that is cross-reactive and protective. However, such approaches often have mixed results, and it is unclear how polyvalency alters the fine specificity of the Ab response and what those consequences might be for protection. In this article, we present a coarse-grain theoretical model of B cell affinity maturation during monovalent and polyvalent vaccinations that predicts the fine specificity and cross-reactivity of the Ab response. We stochastically simulate affinity maturation using a population dynamics approach in which the host B cell repertoire is represented explicitly, and individual B cell subpopulations undergo rounds of stimulation, mutation, and differentiation. Ags contain multiple epitopes and are present in subpopulations of distinct pathogen strains, each with varying degrees of cross-reactivity at the epitope level. This epitope- and strain-specific model of affinity maturation enables us to study the composition of the polyclonal response in granular detail and identify the mechanisms driving serum specificity and cross-reactivity. We applied this approach to predict the Ab response to a polyvalent vaccine based on the highly polymorphic malaria Ag apical membrane antigen-1. Our simulations show how polyvalent apical membrane Ag-1 vaccination alters the selection pressure during affinity maturation to favor cross-reactive B cells to both conserved and strain-specific epitopes and demonstrate how a polyvalent vaccine with a small number of strains and only moderate allelic coverage may be broadly neutralizing. Our findings suggest that altered fine specificity and enhanced cross-reactivity may be a universal feature of polyvalent vaccines.