Do modifications count against the number of item cards a character can star the game with?

Nope, but they're plugged into the weapon(s) you bring and you can't switch them around during the mission.

The limits for items a hero can take into a mission are for Weapons (2), Armor (1), and Equipment (3). Modifications are part of the weapons and are limited only by the slots the weapon(s) have.

· Before deploying heroes to a mission, players may freely give any of their Item cards to other heroes. Item cards cannot be traded while resolving a mission.
· There is no limit to the number of Item cards a hero can have; however, each hero is limited in what he can bring to an individual mission: 1 Armor, 2 Weapons, and 3 Equipment.
-- If a hero exceeds this limit after deploying his hero to the map, he must choose which cards to leave behind. Place the chosen cards aside; they cannot be used during this mission. These cards are returned to the player at the end of the mission.
-- If a hero brings 2 weapons to a mission, when he declares his attack, he must choose 1 of the weapons to use for that attack.