Is it permissible for a man to have sexual intercourse with multiple slave women while having a wife or wives, and does the wife have a say in this, considering what the questioner has read about Ali and Umar, may Allah be pleased with them?

Islam permits a man to have sexual relations with his female slave, whether he is married or not. A female slave taken for sexual relations is called a "surriyah" (concubine). This is evidenced by the Quran and Sunnah, was practiced by the Prophets, Companions, and scholars, and there is a consensus among all scholars regarding its permissibility. No one is allowed to forbid it. Allah the Almighty said: "And if you fear that you will not deal justly with the orphan girls, then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one or those your right hand possesses." And His saying: "And those who guard their private parts. Except from their wives or those their right hands possess, for indeed, they will not be blamed." The wife has no say in her husband owning female slaves or having sexual relations with them.