The fitness effect of a mutation can depend on both its genetic background, known as epistasis, and the prevailing external environment. Many examples of these dependencies are known, but few studies consider both aspects in combination, especially as they affect mutations that have been selected together. We examine interactions between five coevolved mutations in eight diverse environments. We find that mutations are, on average, beneficial across environments, but that there is high variation in their fitness effects, including many examples of mutations conferring a cost in some, but not other, genetic background‐environment combinations. Indeed, even when global interaction trends are accounted for, specific local mutation interactions are common and differed across environments. One consequence of this dependence is that the range of trade‐offs in genotype fitness across selected and alternative environments are contingent on the particular evolutionary path followed over the mutation landscape. Finally, although specific interactions were common, there was a consistent pattern of diminishing returns epistasis whereby mutation effects were less beneficial when added to genotypes of higher fitness. Our results underline that specific mutation effects are highly dependent on the combination of genetic and external environments, and support a general relationship between a genotype's current fitness and its potential to increase in fitness.