No.
You can only use the free sign up bonus and other new player perks only once per casino.
There's a silver lining though. Once you become a loyal player you can benefit from promotions such as free spins on new game release days.
Don't create multiple accounts, since this is clearly forbidden.
In fact, casinos only allow one player account per:
person
household
IP address
So if you have multiple players living under the same roof, you need to play on different sites.