I am working with my employer (non-academic) and have a valid H1B. My employer will be submitting an amendment to my H1B, which will take 2-4 months to approve, i.e. non-premium filling. I want to teach at an university part-time from Jan, 2014. The university wants to applying for concurrent H1B employment. My question is - Will there be any problem in submitting concurrent H1B employment petition by the University if my current H1B amendment is still pending to be approved? Is this recommended? Should the University wait to file H1B till my H1B amendment gets approved? Thanks a lot for your time.