Brutus couldn't. The POD would have to be Cassius not killing himself. The two halves of the army (like the two halves of the Caesarian army) fought and camped separately, and didn't trust/respect the other commander as much as their own. Hence Brutus had trouble keeping them in line and they eventually forced him to attack, where that half of the army would not have done so with Cassius.
Basically, the liberatores just have to wait it out. If they succeed and the triumvirs are forced to attack or retreat due to supply and food problems, the war is all but won. Or alternatively if Brutus is able to follow up his victory over Octavian's on the first day of battle, and control his troops enough to direct them to roll up on Antony from the flank...then there's your victory.
Lepidus, who was likely already in secret negotiations with Sextus Pompeius in Sicily (or at least that's what the accusations from Octavian and Antony claimed anyway) in case disaster struck Antony and Octavian, and I see no reason why he wouldn't immediately seek some sort of settlement after the destruction of Antony and Octavian's army. Nor would Brutus and Cassius reject it.
I'm not exactly sure how things would go from here. The Republic had went more or less 7-8 years without functioning properly, from the civil war to Philippi, and many of the leading conservative statesmen who had been so instrumental and influential in the years leading up to the civil war, would be dead from the civil war or the proscriptions. So I'm not sure how functional the republic is going to be. Alternatively, there really is nobody who can effectively fill the power vacuum, or at least nobody that can (Brutus, Cassius, Ahenobarbus, Sextus Pompeius), has an interest in doing so.
One thing that will be certain though, is there will be a massive demobilization of forces, and the new Republican government will have the same exact trouble the triumvirs, particularly Octavian, had in settling the veterans in Italy (and they had potentially a much smaller demobilization than would occur here, since they had to keep substantial troops on hand because of their distrust for one another and the need to campaign to gain prestige for themselves). If somebody (maybe Antony's brother Lucius Antonius?) decides to take advantage of the discontent from the veterans for not getting land, and from the farmers displaced by the veterans, they could gain a substantial following from Caesar's veterans...