What determines the max. number of tile you can occupy?

The tile limit in Reign of Chaos will depend on a few things but not on your class or any specialty settings. It will depend on the season of RoC you are playing.

Everyone starts with a basic level (usually 20) and this will increase by 1 each day during the event. There are also Expand Plan items that will increase this as well. You can earn there though completing tasks such as those found in the RoC task list (same place you find the daily tasks). Such as the first time you occupy a tile of a higher level. Most likely your friend has completed more tasks.

Check in the Territory tab of the RoC event screen to see if there is a + symbol next to your territory number in case you have earned expand plans but not activated them.

You can also get a increased limit by buying the event specific package. Check the Benefits menu to find this. Depending on your season of RoC this may give you a temporary increase for a week. (which you can renew) or for New Eden you get more tasks to earn extra expand plans over the course of the event.