You need to make sure that the nonprofit employer is a cap exempt employer. The for-profit company needs to file a separate H1B petition next year 4/1/2013.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. Consult with a qualified attorney before making any legal decisions. Gen Kimura, (832) 247-6932.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
The short answer is yes. You may have concurrent H-1B employment as long as both entities file their own petitions. But keep in mind that not all non-profits are cap exempt. It must be a non-profit research entity.
The statement above does not create an attorney-client relationship. It is intended as general information only and it is not a substitute for legal advice. You should consult with a licensed attorney to discuss the specific facts and circumstances of your case.