Will a Music Hall a15.2 drive 4 ohm speakers?

also depends on other ratings for the speaker, like sensitivity. Generally, I stay away from amps that don't have listed power specs into 6 and/or 4 ohms. The power doesn't have to double, but when the power rating at least increases, that is a sign of a good amp design.
It's not that your 4 ohm speaker would sound bad with the 15.2, it just won't open up to its full potential without good amplification.
I really haven't researched truly efficient, high ohm speakers because I have heard several of them at RMAF over the years and did not like them. The sound I prefer (in my price range) is Monitor Audio, B&W, Dynaudio and Quad's L-series, and these are not easily driven. Hopefully someone here can suggest efficient speakers.

My hunch, but it is only a hunch, that your amp should deliver more power at 4 ohms. So, unless you go very inefficient with speakers, you should be ok.

As for upgrading, Music Hall is part of the same audio family along with Creek and EPOS.

At the audio shows, Music Hall amps are typically paired with EPOS speakers and they sound fantastic together. One pairing I heard a few years back that I thought was sublime sounding was a Music Hall integrated with EPOS floor standers and a Music Hall turntable. So, EPOS would be one place I would look.

I am a big fan of Ascend Acoustics and the Sierra 1 . I have used these speakers for almost two years now and they always impress me with their sound.

Your current Quad speakers are no slouches either. What did you wish to improve on with upgrading them or do you just have the itch?

Rich

I think Crouse99 has Polk LS50s, if I read his threads correctly. I do currently have Quads, and I feel the sound is a little bright, but I'm not blaming the speakers. My upgrade path is a new amp (Odyssey or McCormack) or new USB converter (John Kenny JKSPDIF MKIII). Also planning to do some room treatments, but I don't want to over-dampen the room.