Does a Kohen have to seek the same halachic criteria for a peligesh as he would for a wife?
Case one: He is not married (so he's not seeking polygamy). He's simply seeking a "lesser-married status" for the purpose of being with someone who is otherwise not permitted to him.
Case two: He is looking for a second wife. (If so, this raises a new and greater problem with the concept in general: would any child from a relationship with any married man and a peligesh be considered a mamzer?)