In the Hunger Games series, we are introduced to a scant few mutations, or mutts, as they are commonly known. We see those used in the arena by Gamemakers, and are given descriptions of some of those used in the war. We see genetic manipulation used as a weapon several times. It is, however, an incredibly versatile concept; genetic modification could be used in harmless, beautiful ways.
Dogs with fur that is naturally pink, or blue, or any other color. Birds with human singing voices. Centuries of domestication done in seconds in a petri dish. I'd like to advocate for capitol characters to be able to have mutts as pets- within reason. No bioweapons, of course. Just pretty, frivolous things. The Panem equivalent of crazy dog breed mixing.
Whether or not the mutation is too powerful would be at the mod's discretion, of course; that should go without saying. However, as long as it's simply a fashion thing, where's the harm?