I don't believe the rules here are clear. My suggestion: the ATTACKER may place one or more of his planes on one or more unmarked enemy planes and mark the stack with a CC marker. The ATTACKER may also add an unmarked plane to an existing dogfight. The DEFENDER may then place one or more of his unmarked planes on one or more unmarked ATTACKER planes. The DEFENDER may also add an unmarked plane to an existing dogfight. Once in a dogfight a plane may not leave that dogfight until recalled or until all enemy aircraft are recalled/eliminated. Once that happens the dogfight ends and the CC/Melee marker is removed. Just my thoughts.
In my rules for your example, if the ATTACKER engages all the DEFENDER aircraft, the DEFENDER has no unmarked aircraft and so can't initiate any dogfights himself.
The problem with the existing rules is that it's not clear whether both sides can attempt to form the dogfights, and how to resolve a conflict. For instance if the ATTACKER has A1 & A2 engage D1 and A3 engage D2 & D3 while the DEFENDER declares that D1 is engaging A2 & A3, while D2 & D3 engage A1, various planes will end up under multiple CC counters. Because there is no way to resolve that, my rules are laid out so that any plane can be under at most one CC/Melee counter. But there is no indication in the official rules on how the difficulties that might arise should be resolved.
JR