Abstract Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an evolutionary process under varying mutation rates as well as varying fitness is still an open question. Experimental procedures, however, do include these complexities along with fluctuating population sizes and stochastic events such as extinctions. We investigate the mutational path probabilities of systems having epistatic effects on both fitness and mutation rates using a theoretical and computational framework. In contrast to previous models, we do not limit ourselves to the typical strong selection, weak mutation (SSWM) -regime or to fixed population sizes. Rather we allow epistatic interactions to also affect mutation rates. This can lead to qualitatively non-trivial dynamics. Pathways, that are negligible in the SSWM-regime, can overcome fitness valleys and become accessible. This finding has the potential to extend the traditional predictions based on the SSWM foundation and bring us closer to what is observed in experimental systems.