How to add one modifier applicable to different blocks and elements according to the BEM methodology?

Question

BEM

I don't understand, is it possible to do this or not?
For example, I have a lot of different blocks and I want to set common modifiers for them (eg background), but I can't just create a class like .background-beautifull and insert it into the right blocks. But if I can’t do this according to this methodology, then what should I do?