Speakers that work well with Onkyo M-588F/P-388F

Might be worthwhile looking at a kit speaker though I'm not familiar with these. I'm sure there are other A'goners who could assist. Otherwise, have a look at the ATC and PMC speakers - outstanding drivers used in both.

Your are right. Actually, I should have clarified my question by stating that I have access to a custom built
active tube crossover so I am basically looking for a speaker with an excellent driver array and a solid, well-built cabinet. I prefer silk dome tweeters to metal dome.
I listen to almost everything on pretty much an equal bais (but no no rap, hip-hop, punk or heavy metal), but acoustic and electric jazz, funk, soul, R&B, blues, string and orchestral classical, folk, rock, soft rock, reggae, etc. I don't think I really want to pay more than $2000.

I think you need to mention your budget as well as your listening preferences as otherwise you could get thousands of names thrown at you. For excellent imaging and a wide soundstage, I enjoy the Mordaunt-Short Performance 6 speakers (around $5k new) but there are plenty of excellent speakers that will meet your needs at a significantly lower budget. Look at budget models from KEF, Monitor Audio and Epos for example.