On Dragonsfoot, I mentioned an old idea I had twenty-plus years ago for a third alignment axis: Pathos/Ethos. If Good/Evil is how you value the lives of others, and Law/Chaos is how you value the group/community, Pathos/Ethos is what drives you to act on those values.
Pathos is strong emotion -- despair, vengeance, anger, outrage -- that drives you to make the decisions you do, the decisions that brought you into the fold of Lawful Good or whatever alignment you chose. Ethos is calm consideration and steadfast character traits that cause you to behave in accord with your alignment. A Lawful Good character on the Pathos end needs to fight for social order and the common good, while one on the Ethos end is simply Lawful Good by nature, or has rationally chosen Lawful Good. Characters devoted to Pathos struggle with their alignment decisions; those devoted to Ethos are calm in their conviction.
Two characters can both be Good, but diverge on the Pathos/Ethos scale. Compare Angel, the vampire with a soul, versus (older) Superman. Angel is maybe Neutral Good (Pathos); I don't recall him taking a strong stance on the individual versus group issue, but he definitely struggles to protect the innocent, mostly out of guilt and repentance, sometimes out of vengeance, but more and more, as the series went on. out of a sense of connection to those close to him and a genuine concern for the world. Superman, on the other hand, is Lawful Good (Ethos). He's just naturally that good and moral. He can have strong attachments to people, but his attachment to "Truth, Justice, and the American Way" is unwavering.
Ethos is not necessarily Good. Consider some kind of witch hunter or inquisitor, determined to protect the civil order and the church at all costs. Nor is Ethos necessarily Lawful, despite the implications of a moral code. An anarcho-terrorist might be Chaotic Evil (Ethos), willing to kill anyone who stands in the way of total liberation. What Ethos does for both of these is tame their evil, to a certain extent; they don't kill out of love of death and mayhem (that would be Pathos,) but because of strong principles. Either of these extremes would save the lives of those they considered innocents, or of their friends so long as they haven't "crossed the line" and aided or abetted their enemies.
I never really developed this idea, and never used it in play; I didn't feel it was all that useful, and these days I'm happy sticking with a single-axis alignment scheme. Pathos/Ethos wouldn't work well by itself; I think it would have to be used in conjunction with one or both of the other two axes to actually work.