Jamieson, Fausset and Brown on Daniel 11:4

4. kingdom ... divided toward ... four winds--the fourfold division of Alexander's kingdom at his death (Da 8:8, 22), after the battle of Ipsus, 301 B.C.

not to his posterity--(See on Da 8:8; Da 8:22).

nor according to his dominion--None of his successors had so wide a dominion as Alexander himself.

others besides those--besides Alexander's sons, Hercules by Barsine, Darius' daughter, and Alexander by Roxana, who were both slain [Maurer]. Rather, besides the four successors to the four chief divisions of the empire, there will be other lesser chiefs who shall appropriate smaller fragments of the Macedonian empire [Jerome].