Inevitably the Empire will crumble, with or without him. His various sons and nephews especially would become focal points for rebellions and break-away states. Alexander's ego would continue to spiral out of control, ever more self-destructively, and he'd probably end up exhausted/depressed/insane/having lots of nervous breakdowns. After a certain point expansion is no longer possible and he's left chasing his tail north, south, east, and west, just trying to keep his realm together.