Ok, this is what I have so far. Additions, comments, corrections welcomed...please!
Names for Openings
https://www.chess.com/4-player-chess?g=156226-4
h3 d6 h12 l7
Thanks. Any name? I have tentatively named it the 'Sicilian-Kan Black'.
Ok, here's the most recent version. Still looking for more, and comments welcome on any particular opening:

I discovered this move for green (independently, if not as the first one), and play it all the time .
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m8-k8
Specifically with this move order idea:
[Variant "Teams"]
1. h2-h3 .. b6-d6 .. h13-h12 .. m8-k8
2. e2-e3 .. Na5-c6
Ok, two questions:
1) Do you have a name for it? and
2) What do you see as it's advantages/disadvantages
A quick disadvantage that occurs to me is yellow now has an easy, developing, check against you.
1) Icystun-Kujtimi defense
2)
It's the anti-Bg12 variation (which has been very topical in the past) and it stops red from developing the queen immediately.
1) OK.
2) Huh? Whose Bishop can go to g12 and when?
(I still think if your Bishop had taken the pawn you would have won)
The promotion opening is for the FFA Variation.
yeah, that's what I figured. I'm just working on teams so far.
No guarantee, but these should be short Teams games where Red started 1.f4 and Red+Yellow won:
37048, 83135, 122124, 122513, 125068, 5052, 27433, 43352, 48794, 70925, 118737, 135970, 140807, 4711, 9172, 52889, 56163, 63687, 62929, 94611, 103330, 111439, 109694, 122613, 123441, 128401, 129245, 45143, 56987, 63478, 87371, 87687, 90489, 127675, 134342, 139808, 7265, 19352, 22212, 26432, 60318, 63702, 137701, 1942, 2906, 8630, 88194, 88231, 90694, 92100
Add https://www.chess.com/4-player-chess?g= prefix. For example: https://www.chess.com/4-player-chess?g=37048
Short Teams games with 1.g3 and 1-0 result:
7320, 2616, 11926, 14833, 31163, 37832, 47736, 54585, 57470, 56694, 64868, 72884, 72819, 75582, 76038, 81608, 82231, 82802, 85393, 93139, 94111, 94121
And with 1.h4:
4438, 5037, 5085, 5458, 5730, 6341, 6418, 6950, 7767, 1062, 9306, 3560, 1426, 10063, 12699, 12823, 13020, 15414, 14319, 14326, 15707, 16806, 19156, 19964, 21891, 22041, 22270, 24275, 27425, 27542, 26280, 26334, 29270, 29375, 31804, 31797, 34378, 37836, 41433, 40832, 42456, 42727, 44147, 44738, 45362, 47038, 48133, 48658, 47430, 49967
Awesome. Not sure how you chose the 'short', but in the future I would prefer 'long' if that is an option. I figure a long game is one where both sides played well. But I will go through those games looking for good examples and interesting continuations.
OK, so here is where the outline of my book stands so far. This is just the outline, under each section I have the moves written out, the name written out, an image of the position, and some discussion of the advantages and disadvantages. Sometimes I have example games.
Please feel free to send me comments, and if anyone wants a copy of the whole thing as it exists so far feel free to ask me for it.
> But I will go through those games looking for good examples and interesting continuations.
Tell me if there are games starting with different moves. I am not sure I wrote the database query correctly.
> But I will go through those games looking for good examples and interesting continuations.
Tell me if there are games starting with different moves. I am not sure I wrote the database query correctly.
So far they look good. Is the query also capable of searching for higher ranked players? Winning a quick game against a 1200 ranked player is hardly great for illustration.
Higher ranked are 1400+? 1600+? Should all 4 players in a game have high rating? To create a query I need this info.
All players above 1600, game lasts at least 20 moves.
There seems to be a range, from 1400 to 1600 or so, where players are playing what I call 'intermediate'. Below that and they are just stumbling beginners, open to a 'fools mate'. Above that and they seem to have gotten some things down well and are advancing the game. That's how I see it, anyway.
So I class <1400 beginner
1400-1600 intermediate
1600+ advanced
High rated Teams games starting with 1. f2-f4 where Red+Yellow won:
12 moves: https://www.chess.com/4-player-chess?g=80642
38 moves: https://www.chess.com/4-player-chess?g=20952
High rated Teams games starting with 1. g2-g3 where Red+Yellow won:
14 moves: https://www.chess.com/4-player-chess?g=65116
23 moves: https://www.chess.com/4-player-chess?g=24841
23 moves: https://www.chess.com/4-player-chess?g=61316
You called it best-by-test; We should adopt it as Best-By-Test Opening.
The real troll opening is one side queens their pawn and the other goes "f3, kf2," etc.
See 23:30 of this video: https://www.youtube.com/watch?v=ghLLQbmgAXs
Promotion Opening:
1r. g4
1b. d7
1y. h11
1g. k8
All sides move their queen-pawn 2 squares forward to promote it.
I don't believe that is a common idea in teams, as promotion is so much harder.