Third parties are high-risk, same-reward-as-everything-else. In fact, they have the highest risk of any role - if a Townie that enables two power roles and is also a Lover to someone dies, there's still a chance that they can win in the end. Third parties, as a general rule, don't get that luxury and can lose both immediately and arbitrarily. So by nature, they're awful.
With that in mind, when you use a third party, the primary goal is to make the role
fun to play
. There are three general areas I can think of where you can manipulate this.
*How difficult the Win Condition is
*What tools are available to help attain the Win Condition (and, with regard to things being "fun", this is where you can have most success)
*What tools are available to mitigate the risk of the Win Condition
To fill in those slots with a simple example,
*You win when you are the last player alive, or nothing can prevent the same. (This is normally impossible for people who are not in the Mafia.)
*You have a factional kill.
*You will survive the first kill aimed at you.
The risk mitigation aspects are easy to give short shrift because they're contingencies. If a Serial Killer wins without using their 1xBulletproof, it's easy to say "well they didn't need it there, so it's clearly
possible
to win without it and we shouldn't baby our SKs". Don't think that way, but also don't go overboard - an SK that is immune to all kills and a lynch is even worse than one with no protection at all. Strike a balance between keeping the role tough but not so tough that the player feels cheated.
I'm out of time for the morning, so I can't do the detailed post I want, but here's a quick look at the other ways this has been played with.
*Mutually competing Jesters (Mind Screw III) - By having three players with the Jester Win Condition but only allowing one to win, you have increased the risk of the normally-trivial Win Condition and made the role intense (for the people who drew the role, anyway - the rest of the game has to be balanced around this).
*Memetic SK (Mind Screw II and on) - A Serial Killer who gains extra factional kills based on social engineering (in the original case, if the SK could PM the mod the name of one of the abilities in their target's Role PM, they could get an extra kill off on them). This increases the ability of the player to meet their SK Win Condition, and against saps who don't expect it, it's quite an entertaining diversion to trick people into falling into their hands.
*Adaptive SK (Mafia of the Chosen Ones, for instance) - A Serial Killer who gains powers based on other roles used. This and all other "building" roles fall prey to having very slow starts and being very strong at the end, which is usually how you don't want games to go as Mafia has enough of a positive feedback problem already. You either want EVERY role to build like this (Tech Tree Mafia, for instance) or you want to go the other way and make every role limited-shot.
Hell yes I just name-dropped three Tarhalindur games. Despite how his reputation suffered from terrific overreach in the end, he knew what he was doing for a while.
Other ideas offhand--
*Instead of a one-shot Bulletproof, why not a one-shot kill redirection from self onto a Vanilla Townie? Normally Mafiosi figure it out pretty quickly when their kill fails and no one claims Doctor, so etc.
*Alternative and additional Win Conditions are always good to keep in mind. If being the last person alive becomes infeasible, should there be another goal they should try aiming for...?
*Should they even be playing the same game? Bookie is an example of a role where the player takes a bet on how the game will unfold and then has some shot at trying to make it happen. The title character from A Convict's Revenge (highly thematic, but still) had a long list of Win Conditions that were mostly a long list of side objectives that would cause chaos while everyone else was trying to sort out the main game.
Everything you say and do matters. People will respond in ways you may never see. May those responses be what you intend.