I want to cut an opening in the sheet rock to create a doorway for under stair storage. It doesn't have to be very large maybe 3 feet tall. Width is my issue. The wall is at the back of my garage.(the one with the door leading into the house). The wall is parallel to the stairs which lead up to the second floor. The studs are 16 inches on center. I would like to be able to cut one stud to allow an opening larger than 16 inches wide. There is lots of unused space under the stairs and I thought it would be a great place for long term storage. I could stay at 16 inches but that would limit my size on storage containers. Can I cut one stud and when I frame the doorway use additional 2x4's perpendicular to the exsisting studs for support or should I just be happy with the 16 inch opening.
You have 2 issues to deal with.
Structural and fire control.
You need to maintain the isolation of the garage to the rest of the house. Once you open the staircase, you could expose the underside of the stairs and the walls to a breach. As long as you maintain the fire break, you should be okay. You might need to install firecode wallboard.
The studs under the staircase should be just be a partition wall. Verify this before you start removing vertical framing members.
If you want to resale at a later date or cover yourself in case of a fire you will have a lot of work to do. You have to fireblock the stairs, use type x for drywall, and have a rated door, you may get by without having a fire rated door but you need to check with your city or county code.