If units are supposed to stage before responding on mutual aid, like at the foot of a bridge or tunnel, it would make sense to use the box location of the staging location.
Marine units sometimes embark other units, so using Marine 9's home box, for example, will send those units to their quarters.
-Mount Vernon Mutual Aide Box 3826 Staging at Provost Ave & East 233rd St
-Westchester Mutual Aide Box 4400 Staging at Engine 38, Ladder 51's Quarters
-Westchester Mutual Aide Box 3000 Staging at Engine 81 Ladder 46's Quarters
-New Jersey Via Holland Tunnel Box 500 Staging at Ladder 8's Quarters
-New Jersey Via Lincoln Tunnel Box 600 Staging at Engine 34 Ladder 21's Quarters
-New Jersey Via George Washington Bridge Box 1300 Staging at Engine 93 Ladder 45's Quarters
-New Jersey Via Bayonne Bridge Box 5001 Staging at Engine 157 Ladder 80's Quarters
-New Jersey Via Goethals Bridge Box 5002 Staging at Engine 166 Ladder 86's Quarters
-New Jersey Via Outerbridge Crossing Bridge Box 5003 Staging at Engine 164 Ladder 84's Quarters
-Long Island Mutual Aide Box 500 Staging at Engine 313 Ladder 164's Quarters
-Long Island Mutual Aide Box 600 Staging at Engine 304 Ladder 162's Quarters
-Long Island Mutual Aide Box 700 Staging at Engine 314's Quarters