Let’s say Alex’s ilness was something far slower, or that he started worrying about the possibility of suddenly dying. Could he have made sure Perdiccas’s legitimacy as a reagent was more secure? If the regency is strong then so is the child king, and it’s not at all unheard of for former child kings to retake control once they’re of age. Or if Perdiccas simply kills Alexander IV and makes himself king, then the Macedonian empire remains intact, just under the Orontid dynasty rather than the Argeads.
In OTL the reason why the first war of the successors happened was because Perdiccas was making a play to marry Alexander's full sister Cleopetra, and EVERYONE thought that was him making a bid for the throne
So that brought him into a war against Antipater, Craterus in Macedon/Greece and Ptolmey in Egypt, not nesessarily because of any loyalty to the Argeads but because King Perdiccas was likely a mortal danger to those men
In ATL it stands to reason he would have tried to do the same thing: the difference though is maybe he wouldn't have needed to give away so much to Ptolemy and the other generals in the partition of Babylon if his political position was more secure. So I guess King Peridiccas/Queen Cleopetra had a better shot at happening.
But even then though all of Alexander's generals and bodyguards are still out there, and Perdiccas was just not very good at gaining the loyalty of his men nor picking who to trust. His military record against the other Macedonians was also pretty dubious so I think the Perdiccan regime still collapses.
The big difference tho is that the butterflies probably mean Craterus doesn't die in battle against Eumenes. The two men who had the best chance of reigning over a unified Alexendrian Empire for another generation were probably Craterus and Antipater when Alexander died, and Antipater was already in his late 70s.
Craterus was the one man who had both the military talent, prestige and was young enough to have a chance of holding the empire together, plus he was married to a Persian princess who (assuming he doesn't divorce her as otl) his children could be recognized that legitimate by the Persians as well. So he would be kinda like a stronger version of Seleucus Nicator. It would be ironic if the very man who most opposed Alexander's inter-marriage project realize his dream of a mixed Macedonian-Persian monarch reigning over the entire empire.