No, duality is not recognized. Leave the US on a US PP, then try to reenter the US on your “other” one, see how that goes. Also, try to purchase a airline ticket with a non US PP while claiming US citizenship, cannot do it.
Foreign nationals with a visa for work etc can come to the US w/o a pre-existing return airline or other means of planned departure, others (tourists etc) can’t enter the US w/o one (legally).
Officers in the US government service ( state, DOD etc) must foreswear any other allegiance before being commissioned.
As TR stated back in the early 1900s, either you are an American alone or you are not an American at all....(paraphrasing his quote).
Jorge Ramos is a dual citizen.