I mentioned this previously but I believe I may've miscommunicated what I meant. Basically, the influence mechanic is as you said uniquely refitted for the Republic, and that is very nice and makes competing for influence to become Doge enjoyable. However, the influence mechanic currently extends for all titles, no matter how or when they were acquired, as well as what level. Thus, not only would a realm split if there were two or more equally ranked titles as the primary (Kingdom tier in this case) if players/AI spread their influence into different titles resulting in different rulers succeeding each title; but there's an even bigger issue or nuisance where, if a player does choose to expand, they have to spend roughly a thousand influence per county they wish to keep.

This means, if a player were to take say one duchy which included four counties, they would have to spend at least 1000 influence on all five of those titles alone. And that's often at a minimum, as different AI baron-tier vassals and different patrician families will likely compete for these titles. So despite whether or not a player conquers these titles on their own, they do not get to keep them on succession as their own lands.

This also extends to there being a lack of a mechanic for Doges to make Governorships be inherited/landed, which I do believe exists in the Byzantine Empire's Administrative mechanics already and should be easy to borrow.

In an ideal scenario, if a Patrician in Venice were to hypothetically conquer say Krete with a holy war CB; they should be able to keep it on succession without spending influence. Maybe there could be restrictions for using the Republican Army for conquest wars that are not expansion based and therefore do not create new Governorships? Private wars requiring private armies.