Since so many are discussing about applying for TPS Ead while maintaining their F/ H/ J/ other non immigrant visa status at the same time. I'm sharing this link thinking you guys might find it useful in some or other way. I came across this link in another thread of Sajha.

http://www.avvo.com/legal-answers/i-am-currently-on-h1-b-and-my-company-is-applying--2224333.html