Natural selection should favour generalist predators that outperform specialists across all prey types. Two genetic solutions could explain why intraspecific variation in predatory performance is, nonetheless, widespread: mutations beneficial on one prey type are costly on another (antagonistic pleiotropy), or mutational effects are prey-specific, which weakens selection, allowing variation to persist (relaxed selection). To understand the relative importance of these alternatives, we characterised natural variation in predatory performance in the microbial predator Dictyostelium discoideum. We found widespread nontransitive differences among strains in predatory success across different bacterial prey, which can facilitate stain coexistence in multi-prey environments. To understand the genetic basis, we developed methods for high throughput experimental evolution on different prey (REMI-seq). Most mutations (~77%) had prey-specific effects, with very few (~4%) showing antagonistic pleiotropy. This highlights the potential for prey-specific effects to dilute selection, which would inhibit the purging of variation and prevent the emergence of an optimal generalist predator