It depends!
You can only claim one welcome bonus per new company that you sign-up with.
If they offer more bonuses to keep you playing, then of course, you can claim those too.
You can claim all the welcome bonuses from our list if you wish to (unless the brands share a betting licence), but again, once per account (and per household - it's okay if someone else used to live there before, as long as it's your first time living there now).