If every one on the round has called, can the person left of the last to call, raise and make everyone call that new bet?
"could the person after the last to call, raise and make everyone have to call again?"
In the tagged game, Texas-hold-em, no. The person last to call completes the action, forcing the next street to arrive.
There is one exception to this. That's in games where a straddle has been made. The straddle is usually only allowed in cash games and takes place before players have received their cards pre-flop.
A straddle is a blind raise that enables the straddler to effectively buy the big blind, i.e. he gets to put in a blind raise before he sees the cards. If the action doesn't change as it gets to him he has the option to check or raise again. The UTG player is usually the straddler but player in later positions can straddle too, that's referred to as a sleeper straddle.