A second manual should be called the Fiend Folio, for tradition's sake. Yes, an MM2 is tradition as well...but Fiend Folio just sounds better than "Here's this again a second time".
Pulling from what others have (and being away from my MM2 and FF, atm) I'd like a little something like this (again, not near my books so apologies if I mention something that's already in the 5e MM...haven't studied it that closely.)
Elementals & Kin
--Sylph
--Pech
--Triton
--Firebats
--Undines
--a few other some low CR/animalistic things (like firebats) that can be used for the Conjure Minor Elementals spell, besides mephits.
Dragons & Kin
--The Gems (maybe only 3 or 4, at least 3)
--Linnorms
--Gorgimera
Giants & Kin
--Firbolg
--Ice Troll (we don't have that yet, right? Just the normal and marine?)
--Some other giant beyond the big 6...but different enough than just some other terrain type. Though I never much cared for the Verbeeg...they were just [marginally] more intelligent hill giants.
Fae & Kin
--Quickling
--Redcap
--Nymph,
------Naiad/Nereid (I know the nereid in D&D has traditionally been a water elemental, but would be nice if they start doing nymphs properly for once)
------Oread
--Fossegrim (I think they're just way under-utilized in D&D. We need more "guy" fae!)
--Swanmae
Humanoids
--More mid & high level Human type options: pirates, warlords, knights, high priests, etc...
--Somemadeupplaces Orcs/Goblins/Savage Humanoids that are different enough from the "normal" ones.
--maybe a couple more lycanthrope/animal shapeshifter types.
--Dark Stalkers/creepers.
--Xvarts (though are they a Greyhawk creation? Or FR specific? I think they're broad enough to include.)
Constructs
--2-4 additional golem types
--living/crystal statues/caryatid columns
--Mudmen
The bottom line is, even if they're relatively common sounding things we already have (something like "Wunderbar Orcs" or "Otherthere Lions") or creatures that we know from other editions, that they are distinct and different enough from what's in the existing MM to warrant their inclusion.
I do not need/want a bunch of "beholder-kin". You have a couple to choose from. If you want something with 6 eyes instead of 10 or 15 powers in 1 eye or whatever, just do it. You don't need page count for that. You know what the spell effects are. You know what you want it to do. As Nike is fond of saying, Just do it!
I do not need page count for a "Fog Giant, Mountain Giant, Swamp Giant" when we already have Hill and Stone and Cloud and Storm. Take the cloud giant spec's and give them some "misty powers". Poof! You have a Fog giant.
I would LIKE to stay away from setting-specific things (other than FR stuff which is obviously the default assumptions). Leave them for UA articles or setting specific books/pdf's/projects. For example, I thought "They could include Valley Elves and Kender..." but then, in retrospect, I would rather they just go in Greyhawk/DL, respectively, material.
I concur with the observation that the named bid baddies all seem to be getting their debuts in the adventure paths...and I think that works/is working...certainly for them and driving sales. But a free pdf of them, once released should suffice. I agree, I don't need 20 pages of named individuals demons/devils/elemental lords/princes & arch-daemons that demand a certain conceit of the game and planes and multiverse.
I dunno...I'm sure there're more. I'll probably post again after I get home and can really give the MM2 & FF a once over.