The relationship between the dynamics of a community and its constituent pairwise interactions is a fundamental problem in ecology. Higher-order ecological effects beyond pairwise interactions may be key to complex ecosystems, but mechanisms to produce these effects remain poorly understood. Here we model microbial growth and competition to show that higher-order effects can arise from variation in multiple microbial growth traits, such as lag times and growth rates, on a single limiting resource with no other interactions. These effects produce a range of ecological phenomena: an unlimited number of strains can exhibit multistability and neutral coexistence, potentially with a single keystone strain; strains that coexist in pairs do not coexist all together; and a strain that wins all pairwise competitions can go extinct in a mixed competition. Since variation in multiple growth traits is ubiquitous in microbial populations, our results indicate these higher-order effects may also be widespread, especially in laboratory ecology and evolution experiments.