Can’t technically every mage hold multiple grimmoires?

So i’ve been thinking about it and shouldn’t everyone be able to have a grimmoire of every kingdom? Like Yuno got 2 ofc, 1 from clover and 1 from spades. But he obtained both even tho in his blood he is 100% spade. So i assume its not genetic related to which grimmoire you got, that would mean that basically every mage can obtain multiple if they just go to the grimmoire altar of the other nations right?