There are a lot of ways to achieve this.
The earliest, and probably the best, is having a successful Antigonus. At the end, he controlled Anatolia, Syria, the Levant, and parts of Greece under his son Demetrius who was actively engaged with Cassander (and in suppressing rebellious Greek cities IIRC) in Greece up until Lysimachus, Seleuchus and Ptolemy attacked. Plus, Antigonus had attempted to conquer Egypt but failed to defeat Ptolemy in his invasion. So, just have Antigonus successfully defeat Cassander and Lysimachus, not a huge ask IMHO, and have him either succeed in his intial attack on Egypt or have him return after having subdued Macedonia and stalemated Seleuchus. Presto, a Diadochi "Byzantine empire".
Ptolemaic Egypt would maybe seem to be a natural choice for this, but I'm not so sure. IOTL they never seemed especially inclined to conquer regions beyond Egypt. Their conquests in the Aegean/Anatolia and Cyprus seem to have been more about strategic positioning against the Seleucids than outright conquest. Admittedly, this may have rather a lot to do with the incessant waring with the Seleucids in Syria.