I came with a map design idea that could make it more interesting to simulate sending armies on the field and creating sieges. first look at the picture below.
For example, if the Red player want to attack the green player, He needs to move troops in his territory, then move troops in enemy territory and then attack the enemy city.
If blue player want to support green, he needs to move in the field, then move in green territory and then attack the red player.
While in cities, the player is more defended and does not need to pay any food to maintain his troops, but some units like cavalry could be worth less because they are only effective in the fields.
A player could simply keep a city under siege by leaving troops in enemy territory. That could have the effect of preventing that city from producing anything. So the player will be forced to find a way to lift the siege.
Personally, I find the idea very cool!