Alexander would leave military governors that would stay in then conquered territory with a relatively large garrison of troops. Members of Alexander's fighting force came from all over the Greek world, and there really wasn't much of a troop shortage. While Alexander was off east, he'd leave his advisors on the conquered territory, and eventually, these advisors developed strong attachments to the governed territory and after the death of Alexander, stayed out and let the Wars of the Satraps ensue. For example, his Greek advisor Selecluid was placed as governor of conquered Archaemend Persia, and founded the enduring Selecluid Dynasty. The same can be said for Egypt, where his right hand man Ptolemy created a stable Egyptian dynasty.

Yay, something directly related to my thesis.

Alexander was consistent in his pragmatic approach to ruling his vast empire and he displayed a keen awareness of his need to maintain legitimacy through established institutions. This pragmatism was apparent in various facets of his government, including the integration of native nobles into his close circle (e.g. Oxyartes), the continuation of the satrapal system, and the delegation of power amongst his trusted elite (Ptolemy, Craterus, Hephaestion) . Additionally, Alexander installed and supported various regional constitutions which were both in concord with his position as supremely virtuous leader (in so far as heroic, Macedonian, and philosophical kingship - Iliad & Xenophon's Cyropaedia) and the ideals of his native subjects. Alexander also endorsed a policy which enabled him to both cement his position of power by expanding his family and those of his Macedonian entourage, and access to the largest amount of resources possible. Furthermore, he carefully eliminated threats, Persian, Greek, and Macedonian, to his developing pattern of legitimacy using a series of traditional (assassination e.g. Parmenion, execution via established legal routes e.g. Philotas, and in some cases, heroic style murders e.g. Cleitus) methods to ensure his supremacy. In short, Alexander employed various modes of adaptable government, whilst simultaneously assessing their effect on his position as king.

If anyone is interested, I can substantiate (to an extent) these claims.