Polti's 13th Dramatic Situation (Enmity of Kin) includes conspiracy and mutual conspiracy. The conspiracy of one Hating element against the Hated element is just this case. Several elements conspiring one against each other is a conspiracy in which the PCs are going to be simultaneously as Power and Conspirators.
The Power is mostly ignorant of what the Conspirator does until real damage starts happening. Then it is a race against time, trying to find and end the conspiracy before the Power is vanquished.
PCs as Power
The effects of the conspiracy have to begin slowly. At first only a few things seem to be against them, but there have to be enough clues for them to think those "accidents" are connected.
Even in that case the plot becomes more of an Enigma than a Conspiracy.
The Conspirator believes the Power is to be defeated. To keep secrecy, to know who to trust and who not to are the main points for its point of view in the story.
The damage made needs to have a further goal, like preparing the Power for a deposition or maybe to convince it that it's best for it to go away.
PCs as Conspirator
The PCs need to want to oppose the Power but must not be powerful enough to do it in the open.
The result of a Conspiracy may be a Disaster for the unsuccessful part, develop into Pursuit or Vengeance