I'm sure it can, but they usually don't, because once their head is buried, and they are feeding, they just stop when they are full. Remember that saying "I'm full as a tick"? Ticks literally grow into a bubble and by then they are surely felt, seen, or felt and found by the way they make you itch and scratch. Incidentally, I grew up in Texas; ticks were everywhere, and before I'd put my kids in the bath at night after a day outside playing, they would get the "full inspection". NEVER pull a tick out; the head just tears off and stays buried, and then you can get in real trouble. Light a match, let it burn a few seconds, but not all the way down (about a third of the way down) and lay the hot match on the tick's body. He will back himself out, on his own, head intact. You may have to try two or three matches, but I never had to go an more than that. Then, of course, stomp the little booger.
If it re-attaches itself to you then yea it can bite you more than once. For instance if it starts out on your leg and bites you then will your sleeping you move around and it gets aggravated it will move up to another spot and to eat it will have to bite you