When people talk about patriarchy and then it divulges into a complex conversation about the shifting circles of privilege, power, and domination -- they're talking about kyriarchy. When you talk about power assertion of a White woman over a Brown man, that's kyriarchy. When you talk about a Black man dominating a Brown womyn, that's kyriarchy. It's about the human tendency for everyone trying to take the role of lord/master within a pyramid. At it best heights, studying kyriarchy displays that it's more than just rich, white Christian men at the tip top and, personally, they're not the ones I find most dangerous. There's a helluva lot more people a few levels down the pyramid who are more interested in keeping their place in the structure than to turning the pyramid upside down.
Who's at the bottom of the pyramid? Who do you think are at the bottom of the pyramid who are less likely to scheme and spend extravagant resources to further perpetuate oppression? I think of poor children with no roads out of hell, the mentally ill who are never "credible," un-gendered or non-gender identified people, farm workers, modern day slaves...But, the pyramid stratifies itself from top to bottom. And before you start making a checklist of who is at the top and bottom - here's my advice: don't bother. The pyramid shifts with context. The point is not to rank. The point is to learn.