A scenario which has been done before, but I think could be fun to explore.
Let's say that Alexander never falls ill in the summer of 323BC, and his projected Arabian campaign goes ahead as planned, beginning in the autumn of that year, shortly after the birth of his son by Rhoxane. The campaign is a hard-fought one, and Alexander suffers a couple of small defeats, but in the end, the Arabian coastal kingdoms are compelled to submit by the end of 321BC. Alexander spends the first few months of 320BC in Egypt, but falls ill on the way back from another visit to the oasis-shrine at Siwah. He dies near Jerusalem, attempting to return to Babylon.
Elsewhere in the Empire, Antipater's recall to Babylon precipitated the beginning of a Greek revolt, the OTL Lamian war. Historically, the Lamian war initially went quite well for the Greeks before returning Macedonians crushed them in 322, but with no Macedonian return and Antipater absent, they are able to do very well here. The still powerful Athenian fleet is able to handily beat a Macedonian one sent from Cilicia, and an uneasy stalemate continues to exist. The Athenians and Aetolians are frantically recruiting mercenaries at the time of Alexander's death.
Cappadocia and Armenia remain unsubdued under their Persian satraps, and tensions are building in Iran too. Attempted revolts have been crushed in the Greek settler-fortresses of Bactria.
Finally, let's say that Perdiccas remains Alexander's second-in-command, and has retained power in Babylon in Alexander's absence. Young Alexander IV is a boy of nearly three at his father's death, and has a sister, Olympias. Rhoxane is heavily pregnant, and gives birth to a second son, named Herakles, a few weeks after Alexander's death. Ptolemy is Satrap of Egypt, with Seleucus having been promoted to commander of the Companion Cavalry.
So, how do things play out from here?