It should be noted that you must be an E-Verify company when applying for extension, and you need to work in an E-Verify company in the extension stage to maintain the OPT status.
In addition, the following categories of employers can apply for H 1-B without quota restrictions:
University (including all positions, not limited to professors, etc. );
University affiliated or related non-profit organizations;
Non-profit scientific research institutions;
Government research institutions.