I was a Mafioso in a game and the Godfather whom I was on the mafia with used this strategy that will only work under a certain set of perfect circumstances. We won.
THIS STRATEGY IS FOR GODFATHERS
Firstly, it is preferred that you have a confirmed Exe (or at least a Jester that is acting as Exe), so you do not mistake the SK for an Exe. If you are attacked by a Vig and not killed due to your Night Immunity, claim either that you were healed or jailed (depending on which fits your situation). Another way to escape persecution in this particular set of events would be to just claim Exe, but that would completely sabtoage this strategy.
Secondly, it would be important to not say anything in chat until you claim Investigator/Sheriff after you find the SK. I'll go more in-depth on that in the next step.
Thirdly, pinpoint the SK. It is probably necessary that this happens sometime in N1 - N3. Once you have found the SK, claim Sheriff or Investigator (depending on which one you think would work best in your current situation) and call out the SK in chat. If you are claiming Sheriff, say you interrogated *insert name here* and that you found they are SK. If they don't believe you, get the pre-existing Investigator (if he/she is not dead) and have them investigate the SK at night. If you are claiming Investigator, tell the chat that you investigated *insert name here* and you found that they are either SK or Doctor, and ask for said person's role.(OPTIONAL: If they answer Doctor, claim that they are lying and try to get them lynched.) If they are not lynched through that method, tell the Sheriff (if he/she is not dead) to interrogate the SK that night.
Advice: it is best to claim Investigator. This is because if you claim Sheriff and the Investigator is suspicious of you and goes to investigate you, you will be found out as Godfather or Mayor. On the contrary, if you claim Investigator, and Sheriff interrogates you, you will show up as not suspicious.
Now comes the good part. Once the SK is lynched, you'll have a town that's brainwashed into thinking that you're the Sheriff or Investigator (depending on which one you claimed), and unless incriminating evidence is brought forth that proves you guilty (for example, the deaths of both the actual Investigator and Sheriff plus the death of the Random Townie) they will defend you with all of their strength and hopefully (if things work out well) you will win.