Does casting a Partner commander add a the +2 mana cost to your other commander as well?
Each Commander will keep track of its own extra 2 mana separately.


  702.123d Except for determining the color identity of your commander, the two commanders function independently. When casting a commander with partner, ignore how many times your other commander has been cast. When determining whether a player has been dealt 21 or more combat damage by the same commander, consider damage from each of your two commanders separately.