Yes. Section IV(7) of the Commercial General Liability Coverage Form “Separation of Insureds” states:

“Except with respect to the Limits of Insurance, and any rights or duties specifically assigned in this Coverage Part to the first Named Insured, this insurance applies:

a. As if each Named Insured were the only Named Insured; and

b. Separately to each insured against whom claim is made or "suit" is brought.”

See full policy for details.