Sure. Here are a few things I like doing, usually as parts of a larger feedback loop. None of these are really groundbreaking or anything! But, they are things that I find an inverted output gives a different, sometimes better, flavour to.
My favourite thing is bending CV with itself. So feed the output of any CV generator (envelope for example) back into (one or more of) its CV input(s). As is usual with feedback patches, using a VCA (or even better a CV controllable attenuverter) in the CV path allows control over how much gets back into the input.
Inverted outputs are also useful for switching CV between different inputs etc. Basically making simple crossfader/switch type things with VCAs etc. Yes, easy enough to buy these pre-done but I like the flexibility of rolling my own at times.
Audio uses, rather than CV, include filter feedback (fun with pretty much any effect module though) with an inverted output being fed back into the input.
I like this article on neural synthesis by Jurgen Michaelis. Some ideas to take from it. I remember trying to patch something like it on my old 5U system years ago. I don’t think the results were that good from memory. Maybe something to revisit.