Duterte was unique because he lacked such strong connections. Through his mother he was distantly related to several Old Families, but his father was an outsider, with ancestors who came from China. This makes you less acceptable to the Old Families. President Duterte’s predecessor was an Aquino, whose mother also served as president and the one who led the effort to overthrow dictator Ferdinand Marcos. Now a son of Ferdinand Marcos is the leading contender to replace Duterte. The Marcos and Aquino clans are considered Old Families. The Aquinos, mother Corey and son Benigno Aquino III, but tried and failed to make much of a dent in corruption.
The major obstacles for any new president are family and friends, especially if both come from Old Families. The Aquinos are one of a few thousand families that control the economy, and have done so for centuries. This control predates the Spanish conquest of the Philippines in the 16th century. The tribal confederations the Spaniards encountered already had their elite families in control, and the conquering Spanish married into these clans, creating a Spanish/Malay ruling class which persists to this day. These ruling families never fully accepted democracy, which was imposed by America a century ago, after having deposed the Spanish colonial government. The Spanish controlled the Philippines by working with the rich families. It was a feudal arrangement that the United States was unable to change much. The families feud a lot, but will unite to face a threat to the feudal system that keeps them in control. If the new president is going to succeed, he or she will have to prosecute and jail many members of their own class, including friends and family. That's hard to do. When Cory Aquino was president, she herself was not corrupt, but could not bring herself to punish family and friends who were. Any new president could trigger a civil war, or at least a lot of violence because many of the families have private armies), by cracking down on corruption. After all, most of it is among people who are the government. And those people are related to most of those most qualified (by education and experience) to replace them. Many members of the ruling families favor changing the rules, eliminating (or at least greatly reducing) corruption, and making it easier to grow the economy. But many powerful people like things just the way they are.
Duterte was not Old Family and unexpectedly won by promising to do nationwide what he had done in southern city that went from lots of crime to little crime when Duterte was mayor. Duterte kept his promises, including efforts to go after the corrupt officials in the government, who were largely Old Family and could not pull any family strings to avoid prosecution. His successor is likely to be Old Family and the leading candidate is Bongbong (his nickname) Marcos, son of one of the most corrupt Old Family presidents who says he will continue the Duterte policies, except for trying to negotiate with China. --FYEO