Neutral 4 player chess

This varient is a 4 player chess varient, but with a twist.

In all 4-player chess varients I know of, you have either 2 opponents and 1 ally (teams) or 3 opponents (free for all).

In this version, you instead have 1 opponent and 2 neutral players.

The rules are like so:

Your board is the based off @Morkar_the_Northman 's 4 player varient, although I'm much less ambitious about how far my varient will go than he is.

The move order goes white-green-black-brown.

In this varient, though, white & black cannot capture or check brown & green and vice-versa. These colours are considered "neutral" to each other.

White's aim is to beat black & vice-versa; brown's aim is to beat green and vice-versa.

Beating a player is done by a "permanent checkmate", two "temporary checkmates", or a "temporary checkmate" turned into a permanent one.

A permanent checkmate looks something like this:

Where the checkmate cannot be interfered with by neutral players. A permanent checkmate is a win for the checkmating side and both sides pieces are "frozen" while the neutral sides play the rest of their game.

A temporary checkmate looks something like this:

Because a neutral side can block it.

Other temporary mates could involve a smothered mate with the assistance of neutral pieces, or a checking piece that could be taken if a neutral piece was not in the way.

After a temporary checkmate, if the neutral sides are currently playing the sides in the checkmate state are frozen until either the game ends for the other two players or the checkmate is broken. If it is broken, the previously-checkmated player will draw if they checkmate, and lose if they get checkmated again (in any form).

Stalemates can be broken in a similar fashion.

A neutral side revealing a check changes the move order: e.g. if brown reveals a check of white on black, it is now Black's turn and it goes black-green-white-brown now.

While officially the other sides are "neutral", there is nothing stopping people forming informal alliances if they want to.

Does this varient sound fun? Dos it have any major flaws? Discuss.