This suggestion is as follows: in the starting area dialogue, a character has the option to pick an alignment "tendency." The character can skip this if they want, but if they select it, it will shift their alignment a few points towards an adjacent alignment, without shifting it enough to completely change their alignment. Why add this option? Simply to give the player a chance to think a bit more about what kind of character they're playing, and maybe subtly encourage them to do so. Nothing is binding them to stick to their tendency later on in their story, and they can request adjustment later from DMs depending on their character's story arc and class restrictions.
An additional possibility is to give them the option to change tendencies in game whenever they want to. A full alignment change would still require DM approval.
Alignment tendencies are a thing in D&D lore and are acknowledged, for instance, in the setup of Great Wheel Cosmology.
The options would be:
Lawful Good: NG, LN, or
TN tendencies
Neutral Good: LG, CG, LN, CN, or TN tendencies
Chaotic Good: NG, CN, or TN tendencies.
Lawful Neutral: LG tendencies, TN tendencies, NG tendencies, LE tendencies, NE tendencies
True Neutral: can have a tendency towards any alignment
Chaotic Neutral: CG, NG, CE, NE, or TN tendencies
Lawful Evil: LN, NE, or TN tendencies.
Neutral Evil: LE, CE, LN, CN, or TN tendencies.
Chaotic Evil: NE, CN, or TN tendencies.
Again, choosing a tendency does not fully change one's alignment. A Paladin is LN tendencies is still LG, and can still play a Paladin. And again, the option simply exists to prompt the player to think about the character's nuances and guide their roleplay.
I strongly believe this feature would be appealing to players and that a lot of them would bring it into their roleplay.
Just some examples of characters that might fit these tendencies:
LG with LN tendencies: a Paladin of Hoar. He is compassionate and will make a point to help those in need and show compassionate to the unfortunate, but this compassion causes a huge sense of indignation when he sees others hurt, which results in a preoccupation with exacting fitting punishments on the wicked. He tends to show less mercy than other paladins, and where he does show mercy, there is often a harsh twist.
TN with LG tendencies: an honest, hardworking commoner who mostly tends to his own business, but tends to be more dutiful, principled and compassionate than the average person, looking after neighbors, helping strangers where possible, and keeping promises. Now and then he may decline someone in need because he has his own problems to worry about, or fail to keep a promise.
CG with CN tendencies: a rebellious Bard who spends most of his time on hedonistic pursuits and playing pranks on law enforcement, but who will occasionally go out of his way to thwart the plans of authoritarians and tyrants, often through mischief or trickery.
LE with NE tendencies: a cunning politician who adheres to the law simply because it is expedient, not through any sense of loyalty or duty, and will try to change the law where possible to benefit himself. (Contrast this with a pure LE politician, who is self-interested and willing to hurt others, but adheres to the law because he regards it as dignified and respectable.)
NE with LE tendencies: like the politician described above, but will break small laws when no one is looking.
LE with LN tendencies: a guardsman in a Banite regime who is zealously, unfalteringly loyal to a cruel set of laws and strictures, cutting off the hands of thieves and mercilessly collecting taxes leveraged on the poor because the laws of the city demand it.
CN with CE tendencies: a Tempuran who loves the helter skelter of battle, but chooses battles in ways that tend to be destructive or disruptive to the public peace. He'll gladly fight the forces of evil for the glory and thrill of it, but more often than not finds himself getting into fights with Team Good.