Here are responses from Murthy.
Chat User : Can a person, who is already in the U.S. in H-4 status, file 2 H1B petitions (with different employers)? If both petitions are approved, for which employer can s/he work?
Attorney Murthy : If a one files an H1B petition with multiple employers, then s/he can select the employer for whom to work. It is also possible for one employer to decide to cancel or revoke the H1B job offer if it is discovered that the person promised two employers to work in H1B status, with the intention of breaching at least one of the agreements. One must be careful and honest in such dealings.
hat User : I am on L-1 currently. Can 2 different companies file 2 H-1s for me this year? Will there be any problem later because of multiple H-1 filings?
Attorney Murthy : The only risk with this is if both H1Bs are accepted. In such a case one could be using up two numbers under the limited H1B quota. But there is no prohibition under law for a person to file with different employers other than the possibility of a breach of contract when one promises multiple employers that s/he will work on a full-time basis for each employer.