I do not know - but here is one clever thing to improve the situation.
In the picture below you can see a configuration with toilets and washing-hands/mirrors equipment. At the top the small red "circles" are where you spend time adjusting make-up, wash hands etc. And at the bottom you see cubicles with toilets. Each with door and lock.
Gentlemen will enter this facility from left and ladies from right. In the gentlemen area there is also a red box - representing a urinal.
The clever thing is that there is a wall separating women from men. Creating the illusion of two facilities. The wall can be moved if the population contains more women. Or just to let women have more toilets and mirrors.
In the set-up above men have six toilets and the urinal while women have six toilets.
If the event is a ladies-only event you could slide the wall and create:
Now men only have one toilet and the women have eleven! And if it is a football game you could consider to place the wall elsewhere.
To be able to adjust the mix of toilets seems like a simple way of making the situation better. And still there is illusion of totally separated women and men toilets. Which seems to be desired in many cultures/communities. Note also that number of mirrors also changes...
Not sure how common this solution is, but I have seen it in at least one hockey/event arena.