Absolutely men of color face their own struggles. As men of color. White women have a history of abusing men of color for their benefit (Emmett Till, any of the "I was attacked by a black man oh wait no I wasn't tee hee" stories). Which again falls back on the issue of women's agency. Both groups face disadvantages, but they play out in different ways.
I think I understand where you're trying to get with the transitive property, but you can't quantify oppression; hence the term there's no Oppression Olympics. You just can't quantify it because of the ways that race, class, etc overlap.
What doesn't really mean anything? The issue of men being considered disposable still boils down to women being viewed as lacking agency and strength and vim and vigor and whatnot -- all positive "masculine" traits, a dichtomy which relies on inherently defining "feminine" as weak. In no situation is masculine considered weak. There is no inverse there.
Men are viewed by patriarchy as disposable because they are desired for their masculinity. Masculine women aren't desired, only masculine men. Ideally, there would be no war, then no one would be shipped off anywhere to die. But what would people say about a leader who refused to go to war? In this way, men suffer at the hands of men. It's not sexism against men; it's patriarchy back firing on men for valuing masculinity and devaluing femininity. And I don't think you can reverse the two. In no situation is femininity valued over masculinity.
Have I been chasing my tail? Are we back where we started at patriarchy theory?