Can a US citizenship apply for dual citizenship?

Yes. Currently, a U.S. citizen can apply for citizenship in Another Country (i.e. Naturalization) without losing U.S. citizenship.

A person with a US citizenship can become a citizen of another country through any means other than naturalization. Applying to get naturalized when the person is already a US citizen will lead to his/her losing the US citizenship and there will be no way to revoke it.