If I have two Toxicroak in play with the "More Poison" Ability, will my opponent put 4 more damage counters on their Poisoned Pokemon?
Yes, because the Ability says to "put 2 more" and not "instead of".
Source: Sword & Shield FAQ (2020-01-24), TPCi Rules Team (2020-02-06)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH1_124
SWSH1_124