A cap-exempt H-1B doesn't let you work for a "company".
Only universities, university-affiliated nonprofits, nonprofit research organizations, and government research organizations can sponsor one. Furthermore, even after you obtain a cap-exempt H-1B, you would be required to go through the lottery like anyone else if you want to work at an employer subject to the H-1B cap.
Only universities, university-affiliated nonprofits, nonprofit research organizations, and government research organizations can sponsor one. Furthermore, even after you obtain a cap-exempt H-1B, you would be required to go through the lottery like anyone else if you want to work at an employer subject to the H-1B cap.