Yes, Islam permits a man to marry up to four wives at once, but conditions it strictly on his ability to deal justly between them: 'And if you fear that you will not deal justly, then [marry only] one.' This justice concerns tangible matters a man can control — equal maintenance, housing, and division of nights — not the inclination of the heart, for the Quran states that a man will never be able to be perfectly equal in love. The Prophet (peace be upon him) warned that whoever has two wives and leans entirely toward one, neglecting the other, will come on the Day of Resurrection with one side of his body hanging or paralysed, which is reported in the Sunan collections. Polygyny is therefore a permission burdened with serious responsibility, not an unconditional right.
Q&A · Marriage & Divorce
Can a Muslim man marry more than one wife, and what conditions apply to polygyny?
Evidence — the daleel
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Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.