Milk in night feedings?

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I’m gradually transitioning my son from formula to milk. We are at step 1, just trying cut down on bottles and increasing food so he doesn’t end up drinking tons of whole milk. He still wakes up like 2-3x a night super hungry, do you guys give milk during the night? How does that work? I can’t imagine going down to the fridge all night 😩 or do you keep formula for night bottles?