May I submit more than one design in my design patent application?

No, only a single, distinct design may be the subject of each application. Likewise, your drawings should only reflect the views of one design and the entire design identified within a single claim and title. If you have several versions of your design you want to submit, you can attempt to include them but should be prepared for the possibility that the U.S. Patent and Trademark Office will choose to restrict your application to one.