An Eagles set would only make sense if they had Quad mixes in the vaults for the first album and "Desperado" to go along with the two that got released.
But if they're looking into some single Quad releases after the Chicago set comes out, either "On the Border" or "One of These Nights" would be excellent choices indeed!
I agree the Doobies are probably the lowest hanging of the remaining fruit, quad-wise. The band doesn't seem to be averse at all to repackaging/reissuing their catalog, and Warners just did recent hires stereo transfers of all their albums (available at Pono, HDTracks, etc.) so all that would be remaining to do would be the quad transfers. If they were feeling generous they could throw in the 5.1 Scheiner mix of The Captain And Me, and the 5.1 mix of Minute By Minute (mentioned in a WB 'upcoming titles' thing but never released) if the mix was completed.
Beyond that I think the Eagles would be the next best choice, if they're feeling cooperative. Both the first album and Desperado are listed on the 'announced but not released' page of Mark Anderson's quad discography (along with catalog numbers) so it's very possible they do exist. It seems from things I've read (as I'll explain pertaining to Joni Mitchell below) that WB were doing a lot of quad mixing before they actually started releasing quad product. It's hard to really get your head around now, but the industry was moving so fast back then (most artists releasing an album a year, some artists 2 a year) that if things didn't get done quickly enough the album was considered 'old' and they were on to the next one. So it's certainly possible that the quad mixes of the self-titled album and Desperado were in the can but that they put them on the backburner in favour of the new albums at the time (On The Border in '74 and One Of These Nights in '75) and by early '76 Elektra was done with quad so there was no more time to put any more albums out.
Joni Mitchell only had 2 albums released in quad (Court & Spark in '74 and Hissing Of Summer Lawns in '75) but I was reading an issue of Billboard from 1971 recently which had a whole section devoted to quad and it had an interview with Lee Herschberg (one of WB's senior engineers) and he was talking about mixing the Joni Mitchell song 'Carey' for quad. Carey is a song off the 'Blue' album from 1971 so it's possible an unreleased quad mix of the whole album exists, and if it does, it's certainly not out of the realm of possibility that an unreleased quad mix of 'For The Roses' (the album in between Blue and Court & Spark) exists either. On Top of that, 4 of her albums (Blue, Court & Spark, Hejira, and Ladies Of The Canyon) were on the WB 5.1 DVD-A future releases list so there may be even more there.
There are also 5 Frank Sinatra albums (not his best stuff, but great mixes and some fun music), 4 albums + 1 greatest hits + 1 unreleased from Carly Simon, 4 Seals and Crofts albums, 3 Spinners albums (great mixes done by Don Murray who did the O'Jays Ship Ahoy quad mix) amongst others...obviously some of these are more niche than others.