I got this from http://www.emory.edu/ISSP/Scholar/h1b.htm, it says you may be
able to work 240 more days after your current H1-B expires.
Extension:
Your permission to stay in the United States ends on the expiration date of
your I-797 approval notice or your current I-94 Departure Record card.
Extensions up to a six year maximum period in H1B status are possible provided
your department is willing to sponsor you for an extension.
Extension Procedure:
Discuss extension with your supervisor at le