Industrial bioreactors use microbial organisms as living factories to produce a wide range of commercial products. For most applications, yields eventually become limited by the proliferation of “escape mutants” that acquire a growth advantage by losing the ability to make product. The goal of this work is to use mathematical models to determine whether this problem could be addressed in continuous flow bioreactors that include a “stem cell” population that multiplies rapidly and could be used to compete against the emergence of cheater mutants. In this system, external stimuli can be used to induce stem cell multiplication through symmetric cell division, or to limit stem cell multiplication and induce higher production through an asymmetric cell division that produces one stem cell and one new product-producing “factory cell”. Our results show product yields from bioreactors with microbial stem cells can be increased by 18% to 127% over conventional methods, and sensitivity analysis shows that yields could be improved over broad range of parameter space.