I’ve never liked the Alignment system in D&D, but on the other hand, it is hard to extract because it is reflected in so much, like the ideas behind Fiends or Celestials, or spells like Detect Evil or Protection from Law. I’m also not convinced that it’s unsalvageable.
The idea I have is to keep the system as it is but to add the idea that under the categories of Good, Evil, Law, Chaos and Neutrality there are a variety of traits that these things represent. There are a lot of ways to play Chaotic Neutral, for example, though I often disallow this Alignment because it is so often used as justification for a character doing anything with no justification whatsoever.
A character in question chooses at least one descriptor under each of their two Alignment categories. For every session where the player roleplays these descriptors well, they get extra experience points. This is also a way of explaining what is meant by each Alignment in question and for justifying Alignment changes where appropriate. Here are some descriptors I came up with off the top of my head that would make some sense based on what I think of Alignments:
Good: Generous, Chaste, Humble, Peaceful, Honest, Empathetic, Loyal, Kind, Merciful
Lawful: Righteous, Upright, Respectable, Orderly, Legalistic, Disciplined, Authoritarian, Honor-bound, Oath-bound, Traditionalist, Obsessive
Neutral: Balanced, Disinterested, Lazy, Agnostic, Skeptical, Egotistical, Conscientious, Harmonious
Chaotic: Rebellious, Inconsiderate, Individualistic, Iconoclastic, Criminal, Visionary, Innovative, Mad
Evil: Violent, Sadistic, Masochistic, Selfish, Hateful, Intolerant, Vengeful, Deceitful, Backstabbing, Greedy, Megalomaniacal, Machiavellian, Corrupted
Obviously, a given DM can add or subtract whatever they want, and players should be encouraged to come up with their own descriptors.