“Who is an Insured” Clause under the CGL Form

The commercial general liability (CGL) coverage form is supposed to be comprehensive in nature in that all the operations and premises of the named insured are covered unless specifically excluded. But, we have a situation that raises a question about this comprehensive coverage.

Our insured is the named insured on policy A and is designated as an individual. He is also a named insured on policy B as a member of a partnership. If a lawsuit is brought against the partnership at premises owned by the partnership and covered under policy B, can our insured also seek coverage under policy A? The lawsuit names the partnership collectively and each of the partners individually as defendants.