Perhaps a Rega Fono MC phono preamp (roughly $550) or a Rega Aria MM/MC phono preamp (roughly $1,700) and the rest of your budget spent on the best MC cartridge you can find might improve things. Personally, I'd get a Linn Majik LP12, as previously suggested, and start the inevitable climb up the Linn ladder.
Best turntable for the buck
I now amazingly find that my analog system has fallen behind my digital system in SQ and I want to investigate how to improve it.
Currently I have a heavily modified Rega RP3 turntable, with two power supplies, a new platter, sub-platter and other internal enhancements. My cartridge is the Clearaudio Virtuoso.
Not that it’s bad, but I want to look for something that will significantly improve the sound of my current setup.
Will about a 4K investment do that?