Yes, you can still apply for an H-1B and that is a good status to have as it allows for dual intent. In other words, you will be able to start the residency process. Most likely, you will start with a labor certification. It might be a good idea to schedule a consultation with an attorney to determine if any other routes to residency exist for you.
Answered on Jun 27th, 2014 at 11:21 AM