I wanted to keep it simple. All the details do get complicated, beyond even my comprehension (beyond anybody's, as far as I know, genetic science continues to find surprising things on a regular basis). Another semi-sort-of exception is bacteria, which can for instance trade large chunks of genes directly, though, again, not in a very directed manner. There's also quite a few "control" genes that exist where it may be a relatively simple mutation to change the length of an arm, or finger, or even just turn something off entirely, which can cause huge visible changes even though it was just one gene change.
However, in your first case, it sounds to me like you're talking about two changes, each of which are beneficial, or at least neutral. That wasn't what I was talking about, that happens all the time. I'm talking about changing two or three or four (or more) genes simultaneously in a way that each individual change, if applied on its own, would be detrimental, but the whole is an improvement.