Good questions Brandon. The extent to which you make the following changes will all depend on what level of grip exists between just a damp track and a full out-water-flowing-across-the-track rain setup.
Increase caster
Widen front track
Narrow rear track
Raise center of gravity – raise seat/driver and/or ride height
Move weight forward on kart
Loosen floorpan and/or seat bolts to increase chassis flex
Loosen front bumper bolts
Increase Ackermann in steering
Axle change
Bigger front wheel hubs
These are the things I work with. Depending on the rain conditions, I may do them all, or only a couple. Sometimes all a damp track needs is rain tires and maybe a little different track width. The kart can only make up for some of it though, and a good driver who has logged some miles in the rain can do way more than the kart can, in my opinion.
The object of all these changes is to get the front end to grip enough to turn the kart, then keep the rear from coming out in the turn. Much like it is in the dry, only more extreme.
I’m sure some guys have more suggestions, as well as driving tips for the rain. I’ll leave the driving to them, I’m only the mechanic/tuner.