A conceptual model describing a mutating autocatalytic reaction in a continuous stirred tank reactor is analyzed. The mutant is assumed to compete with the original autocatalyst. The phenomenon of multiplicity of steady stares is determined through the application of singularity theory. A mutant-containing feed and a mutant-free feed cases were considered. Eleven regions for the first case and at least 25 regions for the second case of qualitatively different bifurcation behavior were determined using only conditions for isola and hystersis variety. More subregions were identified when applying the double limit variety conditions. The maximum number of steady states which was found for the first case was five whereas the second case showed regions of seven steady states. The yield distribution of the main product and the mutant was briefly discussed for some cases.