Dredge can replace any card draw, not only the one during your draw step.

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.

You can't attempt to use a dredge ability if you don't have enough cards in your library.

If an effect puts a card into your hand without specifically using the word "draw," you're not drawing a card. Dredge can't replace this event.

One card draw can't be replaced by multiple dredge abilities.

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.