The evolution and spread of antibiotic-resistant bacteria have renewed interest in phage therapy, the use of bacterial viruses (phages) to combat bacterial infections. The delivery of phages in cocktails where constituent phages target different modalities (e.g., receptors) may improve treatment outcomes by making it more difficult for bacteria to evolve resistance. However, the multipartite nature of cocktails may lead to unintended evolutionary and ecological outcomes. Here, we compare a 2-phage cocktail with a largely unconsidered group of phages: generalists that can infect through multiple, independent receptors. We find that λ phage generalists and cocktails that target the same receptors (LamB and OmpF) suppress similarly for ~2 days. Yet, a "trained" generalist phage, which previously adapted to its host via 28 days of coevolution, demonstrated superior suppression. To understand why the trained generalist was more effective, we measured the resistance of bacteria against each of our phages. We find that, when bacteria were assailed by two phages in the cocktail, they evolved mutations in , a host inner-membrane transporter that λ uses to move its DNA across the periplasmic space and into the cell for infection. This provided cross-resistance against the cocktail and untrained generalist. However, these mutations were ineffective at blocking the trained generalist because, through coevolutionary training, it evolved to bypass resistance. The trained generalist's past experiences in training make it exceedingly difficult for bacteria to evolve resistance, further demonstrating the utility of coevolutionary phage training for improving the therapeutic properties of phages.