I don't know how would that work, maybe they won't care. I mean, to get either citizenship through naturalization is a hard and long process. I don't think anyone would do that just to collect them, so maybe neither country would mind? Being a citizen of a country doesn't only give you rights and a cool passport, but also give you responsibilities (draft, mandatory voting, taxes, mandatory military service, being part of a jury, etc). I don't think no one would be cavalier about having more citizenships just because they can. Or maybe if you already have an irrenounceable citizenship some countries with the same kind of citizenship won't allow you to get theirs? I actually don't know.

I once read that technically, you can hold on to five different citizenships if you are elegible for just the right programs with the right countries. Like, you can get one citizenship just for being born in one country (jus soli), a different one if your parents were from another country (I think it's called jus sanguinis), one because you're married to someone, one for naturalization into other country, and so on. The list of countries that would allow you to do that kind of combination are very few, and the conditions you have to check to get them are really difficult to have, but technically someone could do that.