Opposites may decide that they still have to kick the sandwiched player together. But:
1) He should get more points than now in similar case and may become 2nd.
2) If we implement "-40 for 2nd Assisted Checkmate" rule, the opposites, at least, will spend more time and exchange more pieces to kick him. Remember that he will earn double points for every capture.
At https://www.chess.com/clubs/forum/view/thoughts-about-possible-anti-teaming-solutions-2018-11-05?page=4 I describe 3 stages of 4PC Solo (FFA) games. And mention that at "3 Players" stage there is imbalance, which we may want to fix.
A player between 2 opposites (for example, Red "sandwiched" between Blue and Green) has worse position due to the board geometry. And if opposites play like a team, that player has no chances to win (be 1st or 2nd).
Does the following rule sound reasonable? "Sandwiched player gets double points for piece captures."
This rule works only while there are 3 players on the board. Two opposites will highly likely attack that player together, so they may capture 2 his pieces while he can re-capture only 1 (and only if there is a chance and his king was not checked). Also there is high probability that before attacking the sandwiched player, those opposites kicked the 4th player together. "Double points" rule should make his chances higher.
What do you think?
P.S.
We can also make this rule conditional. Some of possible conditions:
1) If sandwiched player has less points than other 2 alive players. (He is 3rd or 4th.)
2) If sandwiched player is not on the 1st place now. (He is 2nd, 3rd or 4th.)
3) If the 4th player was not checkmated by sandwiched player. (That also means: was not kicked by opposites.)
P.P.S.
We tested a variation when opposites got double points for capturing pieces (and checkmating) their opposite. It sounds reasonable. The ides was to motivate opposites to attack one another. But if 2 opposites are teamers this rule does not force them to attack one another. They can still attack a sandwiched player together and don't break any rules.