Can you replace a 10W woofer with a 70W woofer?

What does this change in a sound system? I have a 2.1 system that I cannibalized from an old gaming chair that has 5W satellites and a 10W woofer. Would it be possible to replace the 10W with a 70W woofer? Would i have to get a bigger power supply? would the receiver still be ok (just a pcb board i yanked out of the chair and subsequently stuffed into a little box, not fancy at all). I'm a noob with electronics so I doubt it would be this easy, but just curious. Thank you!