2nd better than 3rd is teams. Two players can team for the entire game. I think this should be available as a 2nd option with it's own leaderboard. It could be called classic FFA as it's the original scoring system that was used for the first few years of 4pc. But you cannot replace it with the current system . It's a completely different game.
Disgusting behavior and a case for having a difference between 2nd and 3rd place

that is kinda disgusting but it's only 3 rating points loss
If someone else had been playing it could've been much more
https://www.chess.com/variants/4-player-chess/game/68452851
This is game where I had lost all of my pieces but had a point lead and I strongly feel I deserved to win the game. Yellow had a winning position, but did not have enough points to get 1st. Yellow decided to throw away all of his pieces to screw me out of my win. While yellow's behavior was reprehensible I want to take this opportunity to make a case for 2nd place. I have argued before to no avail that there should be a meaningful difference between 2nd and 3rd in FFA chess. I am not going to rehash the arguments I have made in the past, but want to illustrate this game to show that had 2nd place mattered yellow would have been incentivized to win against blue to get 2nd rather than be vindictive and decide to only stay in the game to hurt me. For those of you who are happy with the status quo of 2nd and 3rd being equal can you at least agree that what yellow did was vile?