Multiple O-1 applications with different sponsors (employers)

[Pesci]

A prospective employer has suggested applying for a O-1 visa before a formal job offer has been made.

If I proceed with the application with this employer, does it mean I cannot apply for other O-1 visas sponsored by other companies?

I want to maximise my opportunities of working in the USA, and the company has an excellent reputation, but I do not want to restrict my options and/or negotiation power if/when a formal offer is made.

If possible, I would appreciate if you would please provide links to offficial sources in your responses to this question. Many thanks in advance for any information provided.

[Pesci]

Also, the same employer wishes to file a H1-B visa on my behalf. So, would the question in the original post also apply to H1-B visas?