The situation was there was a Rule in place that required us to draw an extra card and play an extra card. On the second play, a draw 4 rule was implemented, which increased the Draw from 1 to 4. There was a disagreement as to whether the extra draw counted towards the new Draw total. Should I have gotten to draw 3 extra, as if I’d increased from 1 to 4, or would it only be 2 extra, since I’d drawn 1 plus the extra draw?

A: Essentially, when you have a Rule in play that changes the draw and play by a formula (you get 1 extra draw and 1 extra play per turn, for example) that formula is still in effect on the increased Draw.

If you had Draw 1 and increased to Draw 4, then you draw 3 more cards.
If you had Draw 1 (+ 1) and increased to Draw 4 (+ 1), then you draw 3 more cards.
You can see how that formulaic increase does not affect the number of cards you’ll get to draw on an increase of the base Draw Rule.

See also what happens when you play the special Rule first: What happens if I play a Rule or Keeper that’s not a Draw or a Play, but increases…