I had the same dilema a few years ago. A owned a well respected integrated. I was trying to upgrade one piece at a time and was auditioning a few amplifies. Quite by accident, I rotated a preamp into the chain and was shocked at the upgrade in sound. Secondly, my experience has demonstrated that a preamp is a more significant and impactful upgrade than an amp. I would experiment with upgrading to a stand-alone preamp first.
PS: I speak from my experiences with different equipment than yours so factor this into my comments.
PS: I speak from my experiences with different equipment than yours so factor this into my comments.