I think halacha has two types of marriages and a person can “fully” marry more than one person. A pilegesh is a second “lesser” type of marriage that can be utilized. I’m not exactly sure how a pilegesh wife is different than a full wife (or even a reason why a man would marry someone as a pilegesh rather than a full wife.) But I believe a person can have more than one regular wife without either being considered a pilegesh.
Pilegesh is a difficult Halachic concept. See Ramabam Melachim 4:4
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The Rambam is basing his shitta on the concept that Biyas Penuyah is Assur M’Dioraysa. Other Rishonim (IIRC Rashi) hold Pilegesh is Keddushim w/o Kesubah.