You never do that. Seeking other crew's help to ease your troubles is a sign of weakness and detachment.
When Funzi offered Licavoli a help to deal with Danny, Blackie declined it. He knew the consequences.
Still, you'd arrange something like that, if your amico nostras all alone benefited from death of undesirable.
Albert got killed, because he was stepping on Trafficante's toes, bringing too much heat and out of retaliation. Loyalists like Neil couldn't do much about it, for many big shots were involved. Carlo and Big Paul got the sits at the top, Vito and Ray L.S. made an alliance with Carlo for awhile, Trafficante Jr got rid of competitor and CDG finally got their revenge. What about Frank? He had no problem with anything, as long as money would flow.
But Vincent's situation was all within the family. No conflict of interests. Bonanno wrote, that nobody wanted to go mattresses.
Hypothetically, Albert's crew would have Vincent killed, if he first had Albert whacked.
Frankly, Mangano had it coming. He was in that business from the day one. Two Tommy's were wise enough to share the crown and sword. Same thing he should've done. Go fishing with Joe B, receiving kick-ups from Albert and let him rule the ship.
Many guys in that business rotted in the can or got whacked because of lust for power.