Don’t quite know about 34B and beyond as i never tested it on myself, but you can more or less easily run a 20B model with these specs. I also have a 3060 with 32gigs of RAM and i get around 3Tokens/ second while generating using u-amethyst20B(I believe this is the best, or at least the most popular 20B model at the moment) Q4KM after offloading 50 layers to GPU.
I tried DPOpenHermes from TheBloke(Q6 GGUF version) and i love it but i think there’s an issue with an EOS token as for some reason the model just keep generating text way past where it should logically stop. I see myself using it more but i hope there will be an update that adresses the EOS issue.