How could we end up with the Diadochi successor kingdoms maximally expanding the boundaries of the overall Hellenistic sphere conquered by Alexander, instead of just fighting each other over the territories Alexander previously conquered.
I'd imagine Seleucids having a go at India or Central Asia, the Ptolemids going after Carthage, and a successor Kingdom in Europe going after Sicily, Italy, Illyria or Dacia.
If Perdiccas can keep control over the rest of them, and maintain a united empire, then expansion is certainly possible. Assuming though that this POD is only after the empire has already split, it becomes harder due to the rivalries and the natural urge to fight for the original empire's territory rather than going elsewhere.
Ptolemies - if Ptolemy perhaps arranges a deal in which he becomes ruler of Egypt, but doesn't annoy everyone by running off with Alexander's body, he may be more inclined towards western adventures. I suspect the fear of a Seleucid attack in his rear may have reduced his willingness to commit large forces to a western campaign against Carthage.
Seleucids - if attacks on the other Diadochi are ruled out, then I'm not sure where the Seleucids can go, despite being the most powerful state. In India the rise of the Mauryan Empire makes expansion difficult, and Alexander's own difficulties show that such an invasion isn't to be taken lightly. Arabia is a possibility, but that would be limited to settlement along the coast, as there's nothing worth invading in the interior. Such settlement could however boost Greek trade with India, which is rather more beneficial than a military campaign anyway. Central Asia is also an option, and Seleucus might take up the Khwarezmid king's suggestion to Alexander of a campaign in the Caspian/Caucasus region.
Macedon - no shortage of barbarians, but it depends on whether the rulers see any value in expanding any further to the north. Italy might be more likely, if they decide to help Rome defeat the Samnites and avenge Alexander of Epirus (although whoever ends up ruling Macedon may have less of a connection to him, and hence less interest).