Sure you can apply. Whether you will be considered depends on the company. Your return to the US will depend on when you apply and when the visas are available.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
This is entirely up to the "other" company.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
You are quota exempt. Any other employer can sponsor you for a H1.
Business Immigration Attorney. For H, L, J, EB5s, PERM and EB1/2/3 Petitions. Call 800-688-7892 or visit www.ImmigrationDesk.com. Law Office of Anu Gupta. The advice suggested here is for general information only and not to be construed as legal advice.
You should consult an experienced attorney. Best Wishes!
Attorney: Immigration Law
13295 Illinois St Ste 128
Carmel IN 46032
Ph: (317) 660-6174
Contact (317) 660-6174 for specific legal advice. Answers here are not legal advice because they are of general nature and not tailored to your specific situation. You should not act on this answer without checking with an Immigration Attorney.