1 Kings 4:1 - Joseph Benson’s Commentary on the Old and New Testaments

Over all Israel Reigned over all the tribes, and with the full consent of them all. This is spoken with respect to his successors, who were kings only over a part, and that the smallest part of Israel. Or in reference to the times of division and rebellion under David, when part only went after David, and part after Ish-bosheth, Absalom, Sheba, or Adonijah.