I think Giacomo has it generally correct. My understanding of when things happened, and who knew what and when is outlined below.

Frank DeCicco was blown up in April, 1986. Chin, Carollo, Casso and Amuso are the masterminds behind it, as retribution for Gotti killing Castellano.

In Sept, 1986, Gaspipe Casso is shot twice by the Gambino hit team (James Hydell, Nick Guido and Robert Bering). The hit is believed to be unauthorized by Gotti. It is believed to have been ordered by Angie Ruggiero and Mickey Paradiso due to a beef over heroin money.

In the summer of 1987, Bobby Manna is recorded by the FBI discussing plans to kill John and Gene Gotti in the bathroom of Casella's restaurant in Hoboken. Bruce Mouw and George Gabriel go to Gotti's house and warn him that his life is in danger, and that it is the West Side (Chin and the Genovese). Gotti takes the information seriously, beefs up security and alters his routine.

Casso, Amuso, Gravano and Gotti meet on August 12, 1988 outside Hamilton House (great FBI surveillance poto). I am not aware of any disclosures on what was discussed. I do not recall if Gravano testified about the contents of this meeting. If anybody has info, please share.

In late 1988, an abbreviated commission meeting is held in the Washington Square Village apartments in Greenwich Village. In attendance were Gotti, Gravano, Amuso, Casso, Mangano and Gigante. During this meeting, they claimed to have no hostilities to one another. According to Gravano, Chin dismissed the Manna recordings and subsequent Gotti warning from the FBI, that they were "renegades" and acting without Chin's permission. Gravano claims that Gotti was not fooled.

They also discussed giving commission seats back to the Columbos and Bonnano's. Vic Orena was added but Massino was not due to Chin's concerns about them both being allies of Gotti.

I am not sure if Chin, Casso and Amusa made any direct attempts on Gotti after this meeting. They (Chin, Casso and Amuso) certainly went after people close to Gotti after the meeting. Eddie Lino was killed by the mafia cops in Nov, 1990. Bobby Boriello was hit in April, 1991. I think the mafia cops were also asked to hit Junior Gotti and Nicky Corozzo in 1993, but I am not sure if that is true or speculation.

Most of the info above comes from Raab's book, The 5 Families.