Supplies as of right now are pretty irrelevant and only become more so late in the game, you simply get too much of it and you even get supplies while in foreign territory.
My wishes would be that
#1 You can't resupply when you are not in your own territory. Any bonus to supplies instead increases the amount of supplies you can carry in total. This should also go for loot. You should not be able to gain loot automatically, albeit this time if you are in your own territory instead (no stealing from yourself)
#2 You have to spend supplies to initiate army actions, like battles, sieges, prepare ambushes or build forts. Enable battle intitiation for forced marches, but then double the amount of necessary supplies. Got no supplies and you can only defend and your ranged troops start evey battle with only 25% of their ammo
#3 If you are in allied lands, you should be able to request supplies as a diplomatic action
I am pretty dang tired of "deep striking" AI that marches through several regions from the edge of the map to seek quarrel with me. Supplies should be a safeguard against such actions.