H1 B transfer from Cap exempt organization

[jadoon74]

I am currently working on H-1 B sponsered by a University and it was exempt from the CAP. It started on July 1, 2004 and is valid till June 30th, 2007. Now I have been offered a job from a for-profit company. Can I transfer my H-1B to the new employer even though the cap has been reached for 2007?
If not, is there any way I can accept that job?
I have read a lot about Cap not affecting transfers but is it also true for transfer from cap-exempt H-1b to a for-profit company?
Please reply ASAP