No. It counts the creatures that share at least one type with it. It doesn't count (or care about) how many creatures types they have in common. As long as it is at least one type they all share, they will each get +2/+0
Shared Animosity counts creatures, not creature types. Wether those creatures share one or a hundred creature types is irrelevant. The creature is counted if it shares a type, its not counted if it shares none. Mirror Enitity will be counted once despite having all creature types because it is only one creature.
I have it right?
EDH: RWB Edgar Markov The current updated decklist is here
EDH: WUB Oloro, Ageless ascetic The current updated decklist is here
EDH: UWG Phelddagrif, The current updated decklist is here
EDH: WUB Yennett, Cryptic Sovereign The current updated decklist is here
EDH: WUB Alela, Artful provocateur The current updated decklist is here
EDH: GB Hapatra, vizier of poisons The current updated decklist is here
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)