For the longest time, I was an ardent supporter of just three: good, neutral, and evil. I felt, and still feel, that there is so much ambiguity and grey areas there that no one is ever truly just lawful good or chaotic good. It depends on mood and scenario, and people shift through that spectrum all the time. So I preferred general larger umbrellas of general moral leanings.
But I have since changed. Even with good/neutral/evil, it still really doesn't capture things well. People tend to play their PCs with their own moral influences anyway, regardless of the alignment on the sheet. And people who are disruptive will still say "I'm just playing my evil character in accordance with their alignment!" And then it still doesn't address how certain mundane humanoids are inherently "evil" when they might not be.
So I've changed more to Moorcock, B/X version of law/neutrality/chaos. Law/neutrality/chaos are all cosmic influences that have touched the creature in some way on an individual level. Are you lawful? That means you have been influenced by forces of law (which include most traits we define as "good", but how you implement those good behaviors is up to you (greater good, follow rules, work outside the rules as long as the bigger society benefits, etc). And if you're touched by chaos, you tend to want to sow discord and confusion. You want to break down societies norms and rules for the sole benefit of your enjoyment.
That way, you can have a tribe of orcs touched by chaotic cosmic forces, but that doesn't mean all orcs are chaotic or evil. it depends on what cosmic forces have had the influence on you and/or your society.