Can a regional airline pilot fly for a regional airline AND be a gate agent in order to make extra money?

Could a regional airline pilot have 2 jobs for the airline, be a part time gate agent and pilot?

Yes, as long as you can meet the rest requirments for the pilot portion of your job.. To oversimplify a very complex rule, you have to have at least 24 hours off every 7 days, and must have a specified number of hours of rest before you can begin a flight assignment.