Yes.You can have more than one H-1B status petitioned by different employers. But you cannot start to work for the new employer until we file a new H-1b petition if you are already in an H-1B status.

Can I get H-1B from a private company while I am working at a college as a teacher?

One more question: will my second H-1B be subject to the so-called quota?

Yes. However, your college teacher H-1B is a CAP exempt one. Thus, unless you went through a CAP selection before and have a H-1B Quota already, you need to wait until next year to apply for the CAP H-1B, and then start working for this private company.