As Capeci says in the above link I posted, the Outfit's representatives started skipping more and more Commission meetings in the 1960s. He said the result was effectively a two-headed Commission with Chicago resolving disputes between families west of them. He did say New York and Chicago continued to maintain regular contact, due mainly to their interests in the Teamsters, Laborers, and Hotel Employees International Unions.

By late 1985 I doubt the Outfit would have been inclined to get on the phone and tell Gigante, of all people, to get his house in order. Though, on a side note, we know from Al D'Arco's testimony that the Genovese had a member designated as "il messaggero" - a messenger between the Genovese and Chicago families.

In more recent times Bonanno soldier Vincent Amarante was running a strip club in Chicago before it was busted in 2000. The general consensus seemed to be that it was with the Outfit's OK. Another Bonanno soldier, Vinny Faraci, was involved in the Outfit-run Crazy Horse Too strip club in Las Vegas before it was raided in 2003.