Change visa status without secured employment

I currently have an instructor visa (ALT).
Can I apply to change it to a Specialist in Humanities (to teach eikaiwa) without having secured employment?
I recently had an interview and the eikaiwa urged me to apply to change my visa status ASAP.
I assumed I couldn't apply to do until I had a contract from an employer.

That is also my understanding. You need a firm offer from the eikaiwa to apply, AFAIK.