Concurrent H-1B

I am currently on H-1B with a university (cap exempt), working full time (40-hrs/week). An opportunity has come to work part-time for another For-profit institution (not cap exempt), may be for 20 hours or so per week. So my questions are: Can I apply for a concurrent H1 (For-profit; not cap exempt) whose work load will be additional to my current H1? Is there a restriction on where the concurrent H-1 sponsor is located in the US? Does 'Concurrent H-1B' need to go through the yearly quota since it is 'not cap-exempt' in my case?

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ANSWER: 

The last time I checked into this issue, you could apply for a concurrent quota H-1 even though you are currently holding an exempt H-1. Location of the employer is not important, location of the job is.

Unless the context shows otherwise, all answers here were provided by Rajiv and were compiled and reported by our editorial team from comments and blog on immigration.com

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