Maybe Kyriarchy works better for you? It describes a multi layered and interactive web of stacked series of oppressive factors that encompasses race, class, gender, sexual orientation, ablism issues etc.

Though under the definitions of patriarchy men are still oppressed. Young men and the poor are held in sway and looked at as disposable pawns and labor by the patriarchs - powerful men in the lead positions, like male heads of the family, but in this instance the ‘family’ is government, military, businesses and corperations, guilds, unions and bosses. The the buy in for those men at the bottom is that even a lowly man gets to feel like they are better at least than women. The act of being a woman is an automatic sort of failure state. Hence why men behaving in a feminine fashion are a threat. It subverts the hierarchy when someone willing chooses to behave as “lesser” of their own volition and seem happier for it.