Looking for suggestions on speakers and an integrated amp for a second system.

I am thinking the loudness control would be helpful. May eliminate (maybe not entriely) the need for a subwoofer.

Yamaha and Vincent made integrateds with that feature. I am sure there ore others. 

Look for speakers with wide dispersion. Ones that serve an area larger than the lisening chair. 

This may not sound very "audiophile", but give some thought to a tube integrated like Line Magnetic, Rogue, ARC, etc. and some Heritage Klipsch speakers - some older Heresy or Quartets or Fortes.  You can often find the 1 and 2 versions of these well under $1K then put the rest into the integrated.

Most people think of Klipsch speakers as "rock speakers" and that they are bright and unrefined.  That's true (IMO) when they are played loud with rock, but they can be quite special when played at reasonable volumes with female vocals and acoustic instruments, especially guitars.

I second the recommendation for a small subwoofer.  Something like a Rythmik L12 or a SVS SB-2000 will add presence to the music.

If I were starting from scratch with that budget I would look at Kef LS50 wireless speakers and mate them with a Rythmik Audio F12 sub (or maybe look into REL or even Kef's own subs but I think the Rythmik will give you more bang for the buck).

I am quite familiar with the LS50 sound (paired with a REL T/5 sub).  You are probably not going to find anything in the $2500 price range (estimate for the Kefs) that comes close (speakers plus amp and all the cables, etc.).  That will give you $1200 to find a decent sub(s).

You can put a lot of fantastic systems together with $3,700. I'll throw out one option; get a Belles Aria integrated and a pair of Vandersteen 1ci speakers. You could be happy with this system for years to come. Good luck!