The Chicago Outfit dealt with one Family in New York. It was the very powerful Genovese Family. Jack Cerone went to New York at least a couple of times to meet with them about some kind of Union thing that also involved Chicago. I never heard of the Outfit really interacting with any Family in New York except the Genovese Family. I know the Outfit Bosses did not care much for the Bonnano Family at all. again, This was over 30 years ago.