Mainstream D&D has rarely if ever interrogated the distinction between alignments as ways people behave and alignments as cosmological factions. In the Implicit Empire, each alignment gets its own set of deities, extraplanar beings, etc., etc. Now, “filling out the grid” can be very creatively fruitful; I wrote about this in my Designer’s Notes article for GURPS Deadlands: Varmints. However, it’s possible to go over the top on this kind of thing (demodands, anyone?) It seems like you could pull some interesting world design out of assigning cosmological significance to only a few of the alignments.
The obvious implications are worlds where Good struggles against Evil, and law and chaos are basically stylistic, or worlds where Law struggles against Chaos, etc. However, you don’t need to set up a bipolar world. Consider some other possibilities:
Good/Lawful Evil/Chaotic Evil: This is arguably implicit in the baseline world set up by the original 1e books; the good races and supernatural beings seem to be able to come together to oppose evil, while demons and devils are at constant war when not trying to conquer the Prime Material. The neutral alignments, meanwhile, have minimal supernatural backup until later books when TSR started filling in the grid.
Lawful Good/Chaos/Evil: This would be good for a world where Good is constantly hampered in its battle against Evil by its inability to pull the stick out of its rear and make common cause with Chaotic rabble.
Chaotic Good/Lawful Evil: Some friends and I played a game of Lexicon called Vespers, about a world riven by struggle between the Brilliance, a chaotic good faction, and the Shadow, its lawful evil counterpart. So groups usually near the center of their alliances, like paladins and demons, were divided between the cosmological factions, not really comfortable anywhere. Slaadi and elves, fighting side by side. It was a really interesting world design challenge.