It’s also possible for two mutations that would be neutral if either one occurred by itself to be non-neutral if both occurred together.
For example, in the standard genetic code mutating the codon CGG->AGG doesn’t change the amino-acid in a protein, since both triplets code for arginine. Nor does mutating the same codon CGG->CGC, since that also codes for arginine. So both these mutations are likely to be neutral. But having both mutations together, CGG->AGC changes the amino-acid to serine, which may not be neutral.
Whether a particular mutation is beneficial, neutral or detrimental depends not just on environmental context, but also on the presence of other mutations.