No, you may only submit one application per season. St. Andrews will check for duplicate applications and all duplicate applications will be deleted, so it is very important that only one application is submitted. You can submit an application for both the High and Shoulder Seasons if you wish, but again only one application per season.
The lead golfer name cannot be changed on Advanced Application tee times. This means that you cannot have friends or family members submit applications for you and then change the names if successful.