In 168 BC in OTL, Antiochus IV of the Seleucid Empire marched down the Levantine coast and was preparing to invade Egypt with a great host. He likely would have succeeded, had the Romans not sent an ambassador named Gaius Popillius Laenas to turn him aside. Laenas met Antiochus near the Nile delta and drew a line around him in the sand; if Antiochus did not decide to turn back before stepping outside the circle, he would face Rome's wrath.
In OTL Antiochus considered for a few moments (or maybe minutes), before deciding to turn back, leaving Egypt to the Ptolemies. Now let's say, with a POD of a hangover or bellyache or diarrhea, Antiochus is in a bad mood, and decides to say no (or perhaps even executes Laenas on the spot); he invades and subdues most of Egypt before the Romans can arrive.
Now, can he keep Egypt under control under a governor, or will he install a puppet (or even false) Ptolemy to rule it? In how strong of a position are the Romans, and can they really threaten his holdings in Asia Minor, Cilicia, Syria, and Judea?
If Antiochus does this then he will have the wealth of Egypt to lean on, and butterflies flurry away his death due to disease four years later. Since his rule was the last strong one of the Seleucid Empire, he can spread his ideals and strength to his son (maybe), who was an infant at his father's death IOTL; with this POD Antiochus can live very long (he is from a long-lived family), and his son will be an energetic young man when he assumes the throne.
Another interesting situation of note is the continued persecution of Jews. Antiochus tried to Hellenize Judaism, associating Yahweh with Zeus and then both with himself (as he was considered a god by most of his subjects' religions); of course this backfired, but do you think that, with more time and force, the majority of Judaism will be hellenized, or most Jews will leave Judea for freer places such as Rome and Greece?