The Diadochi (/daɪˈædəkaɪ/; plural of Latin Diadochus, from Greek: Διάδοχοι, Diádokhoi, “successors”) were the rival generals, families and friends of Alexander the Great who fought for control over his empire after his death in 323 BC. The Wars of the Diadochi mark the beginning of the Hellenistic period.
…
How many successors?
Five Diadochi Dynasties
Due to the influence of the Prophecy of the Book of Daniel, chapter 8, many Christian commentaries state that there were only four primary diadochi. In truth, however, there were at least five primary dynasts throughout this period: Lysimachus [Thrace], Cassander [Macedon], Ptolemy [Egypt], Seleucus [Persia], and Antigonus Monophthalmus [Asia Minor].
After the Battle of Ipsus [301 BC], Antigonus was killed, but his son Demetrius took a large part of Macedonia and continued his father’s dynasty. Never during this period did only four diadochi control Alexander’s former dominion. After the death of Cassander and Lysimachus, following one another in fairly rapid succession, the Ptolemies [Egypt] and Seleucids [Syria] controlled the vast majority of Alexander’s former empire, with a much smaller segment controlled by the Antigonid dynasty [Macedon] until the first century.
It was one of four dynasties established by Alexander’s successors, the others being the Seleucid dynasty, Ptolemaic dynasty and Attalid dynasty.
The Attalid dynasty (/ˈætəlᵻd/; Greek: Δυναστεία των Ατταλιδών) was a Hellenistic dynasty that ruled the city of Pergamon after the death of Lysimachus, a general of Alexander the Great. The Attalid kingdom was the rump state left after the collapse of the Lysimachian Empire.
So, in the free-for-all after Alexander died, there were not really four successor states. There were a dozen-odd, then five, then three: Macedon, the Ptolemaic Empire, the Seleucid Empire. And maybe you can count Pergamon as a fourth.
If you do, though, wouldn’t you also count Epirus as a fifth? And what about the Pontus, and Galatia, and Cappadocia? The Greco-Bactrians? The Indo-Greeks?