So, I'm doing these because I think that some of us (not me) will improve by looking at other games and figuring out what works. That's, like, the basis of the development of regular chess. What I mean is that, the more of these that come out, the more established a four-player chess game will become.
This one is incomplete because I was going back-and-forth on the in-browser interface, took a break, and my Windows did the I'll-restart-right-now-to-show-you-who's-boss. But, the opening is worth looking at. Spoiler: I lose.
Red starts off with 1) g4, d6, d11, k11; 2) Nf3, d5, d10, j11; 3) g5, e6, d9, i11; 4) g6, d11, d8, h11; 5) g7, Bb5, Ni12, g11=Q';
As you can see, move five is about the earliest you can receive a queen. With the Michael Bay opening, you can run a strong drive up the rook file. It's best to do this when the Queen side faces the preceding movant. If the Kingside faces the preceeding movant, then you expose yourself to a little bit of easier mating from those who can cause you the most pain. 6) g8=Q', Nc9, k12, Q'l6; 7) Q'd8, c4, h12, Nl4; 8) Q'h4, d7, Bh13, Q'k5; 9) Q'd4, Qa6, j11, Nl9; Red's queen prime is looking to trade for Blue's queen.
9) j3, Nc6, j10, Q'k10; Blue's knight is now attacking Red's promoted queen after sidestepping her attack. 10) Qh4, e7, j9, Q'xj9; 9) Bj2, f7, Rj14, Q'xj14; based on the point value difference, a trade of a rook for a promoted queen makes some sense. But it also can result in tactical disadvantages against the other two players.
11) Bh3, Qa7, Nxj14, Rn10; I moved my rook over to prepare to push my m10-pawn up to the top. Red's got a solid game because Red is going to pivot with the rook, two bishops and two queens to attack which ever adjacent opponent is weakest. 12) Qg3, Qb6, Ni12, l8; 13) Rg1, Qa7, Ng11, k10; 14) Q'g4, Nd7, i12, Bm8; The bishop is an attempt to protect the Green's night, which is vulnerable.
15) Bxm8!, d4, i11, Qxk10; 16) Q'h3, e5, i10, l7; 17) Ni3, f6, i9, j10; Green would have been better off with a Bm7 followed by a 0-0, because then the Knight would not have been the giant liability that it is to become. 18) Q'g2, Qb6
So, that's the end of it. But, if you look at chess history, most of the early games play like we do when we're first learning how chess works. It's not until a record of chess games became long and accessible that the moves reached a greater and greater depth. If we do the same early with four-player, then we have a chance of a making this sustainable.