"So only men are allowed to keep multiple partners or are you okay if women do the same?"
We're Muslims and we follow the Quran and the teachings of the prophet, Allah has permitted men to marry 2,3 or 4 but if the husband can't be just with all his wives than he should just marry 1 wife.
"Healthy relationship" that's quiet subjective, you make it seem as though all of them are under one roof.
If the man has wealth and can equally treat his wives the same than he can marry 2,3 or 4, each family has their own home and it depends on the husband how he shares his time between them all.