Golgari Thug

Once you've announced that you're applying a card's dredge ability to replace a draw, players can't take any actions until you've put that card into your hand and milled cards.

If you're drawing multiple cards, each draw is performed one at a time. For example, if you're instructed to draw two cards and you replace the first draw with a dredge ability, another card with a dredge ability (including one that was milled by the first dredge ability) may be used to replace the second draw.