Social and Personal Alignments

Give characters and intelligent monsters two alignments.

Their Social Alignment is how they behave due to culture or obligation. It's mostly a role-playing aid and somewhat subject to change based on circumstance.

Their Personal Alignment represents their core beliefs. This is how they'll act in times of stress, low morale, or surprise. It is their "true colors", and if your game has alignment-detection spells, what they will reveal.

If an NPC has conflicting alignments, as a GM you can play them off each other to create a more nuanced interaction with relatively little effort.

For PCs, this can present another convenient role-playing aid. I think a lot of players do this implicitly for their characters, anyway.

Non-intelligent creatures, or those strongly associated with a particular alignment, like angels and demons, probably still only have one alignment. Sometimes multiple alignments could still make sense in this case. The trope of the fiend who acts civilized but descends into a fury when their plans are thwarted could be represented by a Lawful Evil social alignment and a Chaotic Evil personal alignment.

You can tack this onto pretty much any game that uses an alignment system. Maybe not LotFP, or other games where alignments are cosmic forces.