The independent evolution of different quantitative traits is often thought to require a modular structure of the genotype-phenotype map (GP map). In that context, pleiotropy is considered a constraint on adaptive evolution. Previous studies have shown that even though a pleiotropic GP map can avoid unfavorable genetic correlations among traits, pleiotropy still impedes evolution across multiple generations. In this study, a linear model of the GP map is used to investigate the effects of pleiotropy on the evolvability of quantitative traits. An R script is made for population simulations of two quantitative traits under conflicting selection pressures, by means of which a variety of GP maps of different levels and types of pleiotropy are compared, both mutually and with modular GP maps. In addition, the predictive power of quantitative genetic measures of evolvability is tested. The results show that GP maps with extensive pleiotropy can be equally optimal as modular ones, implying that evolvability does not require modularity. Examples are provided both where pleiotropy constrains and where it enhances the response to selection, depending on underlying assumptions of the GP map. It is further shown that quantitative genetics theory can accurately measure evolvability, even when genetic correlations and conflicting selection pressures are present. In addition, other properties of the GP map affecting evolutionary response are considered.