The problem at this stage is, there is not one, but three precedents of pretty much dictatorship in Rome. There is Marius, Sulla, and Caesar. It would be only a matter of time before there is fourth.
First, let's decide on how total the assassins' victory is. Let's presume they win a crushing victory, and Anthony and Octavian are dead or otherwise removed. I presume this is the scenario you are going for, right?
Second, let's decide on if they manage to get along. Let's presume they get along for at least the next ten years. I doubt that either Cassius or Brutus would start another civil war too quickly.
Third, who else remains. Sextus Pompey is still at large, and he might be able to get in legitimately. So, there is your new Triumvirate - Cassius, Brutus, and Pompey. After all, they can become convinced that the Senate is simply allowing the Republic to drift from one catastrophe to another, with predictable consequences.
My end prediction is, by about 35 BC the Republic is fully controlled by the New Triumvirate, with Cassius and Brutus drifting increasingly more suspicious of each other, and Sextus Pompey holding them more or less together. I see Pompey as the most ambitious of the three - Cassius and Brutus are more of demagogues, but they are not as popular in Rome itself, and as such, their control depends largely on their influence on the Senate. Pompey, on the other hand, is charismatic, a proven naval (!) commander, has name recognition thanks to his father, and is the most likely to engage in any kind of foreign adventures (Egypt sounds very likely here). Ultimately, I would imagine that Pompey would somehow take advantage of the situation, and barring extreme bad luck, he might be able to outmaneuver the other two.