Competing species use a variety of strategies to gain an advantage over a competitor. We show that a desirable auxotrophic mutant can sometimes gain a growth advantage over its parental (or, wild-type) organism by using an offensive inhibitory or lethal strategy against the parental organism that lower’s the parental organism’s growth rate. Our numerical results indicate that inhibitive offensive strategies can stabilize a system while lethal offensive strategies can destabilize a system. Thus, even though a mutant may have a lower growth rate and/or higher metabolic needs than the parental organism, it may gain an advantage over the parental organism if it can limit the parental organism’s growth allowing it to coexist with the parental organism.