In general, you cannot apply for a U.S. work visa without a specific job offer from the U.S. Additionally, the application is handled by the U.S. employer and not by the foreign employee. An application independent of the U.S. company that is acting as employer is thus not possible.
However, the O visa is different from other work visas in one respect:
Not only U.S. companies, but also U.S. agents can act as petitioners. This way, the beneficiary has the chance to work for different employers via the U.S. agency. If, however, a company acts as petitioner, the beneficiary can only be employed there.