The FBI running a psyop to get the Sicilian mob to attack CPUSA might sound far-fetched. Meet HOODWINK, a COINTELPRO operation to do just that (thread)
It all started in 1966, when the NY FBI office came up with the idea. Bureau leaders loved the idea and gave the green light to begin pitting the two groups against each other 
The first move was to put together a flyer against the unjust labor practices of the Arrow Linen Supply Company, a Cosa Nostra (the Mafia) owned business. They made it appear to be by CPUSA, and that flyer was then mailed to Arrow Linen Supply Company.
The FBI then moved to make a more direct attack. CPUSA headquarters had been bombed, and in the Party's statement they referred to the bombers as 'hoodlums'. The FBI decided to try and spin that as a reference to the Mafia, as if CPUSA was blaming them.
The FBI sent three anonymous letters to Mafia leaders, appearing to be from CPUSA members, blaming the Mafia for the attack and threatening retribution. FBI headquarters approved the letters and encouraged more action.
I haven't figured out whether this was ever carried out, but they considered inserting a sentence into a column in the Daily News. Charles McHarry, the reporter whose article they would put it in, was often used in this way by the FBI.
FBI headquarters suggested using a Longshoremen's union dispute which CPUSA was involved in to further HOODWINK, but the NY office said it wasn't possible at the time
In August 1967 the FBI sent a letter attacking the Mafia to the editor of The Worker, the CPUSA newspaper, posing as a reader in hopes that they'd publish it. The FBI then planned to send copies of the issue where it was published to Mafia leaders along with threatening notes.
While The Worker never published the letter, that same month it appears Philidelphia FBI cultivated an asset in CPUSA and got him to snitchjacket a clean CPUSA member. It's unclear why exactly this was HOODWINK related, but it seems the asset may have also had Mafia connections
Me: "maybe this document will clear things up... oh..."
NY FBI wanted to send a letter to union offices from a worker claiming his brother in law was a commie & letting union officials know that on orders from Moscow the communists were going to try to get organized crime out of the unions. The FBI knew this had "no basis in fact".
FBI headquarters was beginning to realize many of the HOODWINK tactics had been ineffectual, and only approved sending it to local teamsters in Philadelphia. The next document is hard to parse, but it appears a (former?) teamster was an FBI asset and recieved the letter
They appeared to have some success with the letter, but the redactions prevent us from finding out what that success entailed. FBI headquarters denied the NY request to send another letter, as they felt it would cause the source to lose credibility.
In May 1968 NY wanted to send another letter to the editor of The Worker from our good friend I. Cohen (same as the first letter to the editor) again attacking organized crime. This letter was never sent, as it was decided that HOODWINK was ineffectual and the op was discontinued
While this operation ended up being completely ineffective (as so many were), it's still incredibly disturbing. The Mafia of course dealt brutally with its enemies, and the FBI was attempting to use them to slaughter a peaceful group of communists.
