Personally, any augmentation to the Skill system should: first, not overwrite the existing proficiencies and skill system in place, second, not be long, ie. Pages upon pages of skill specialities written up like feats or spells and third, not be overly complicated to adjudicate.
So, I'm tempted to try an import something like FATE's stunt system as a way to define specializations within skills. What I especially like is how they're written up as a Mad Libs appproach and that they add a justification from the character, so they feel personal.
For example:
Because I am proficient in
[skill] and
[something about the character, backstory or class, etc], I can
[use this skill in a specific fashion in certain circumstances].
So what are those specific fashions?
- Use an non traditional ability score, like using Strength in place of Charisma for Intimidation.
- Use one skill where another might be more applicable.
- Do something faster. So like Cunning action, but more limited. Maybe an Illusionist Wizard can use Arcana to identify illusion spells without having to use their reaction, if you use Xanathar's rules for spell identification.
- Auto succeed certain things. I'm thinking acrobats not needing to make a check to balance on a tightrope, for example.
Certain Circumstance is a safety valve to make sure the stunt isn't too spammable.
So, to have some written examples:
- Because I am proficient in Arcana and [am an Illusionist Wizard], I can [use Arcana to identify Illusion spells without using a reaction].
- Because I am proficient in Intimidation and [am an Orc Barbarian], I can [use Strength instead of Charisma when intimidating an NPC smaller than me].
- Because I am proficient in Acrobatics and [was raised in the Circus], I can [walk along narrow surfaces without having to make a Dexterity (Acrobatics) check].
- Because I am proficient in Performance and [am a gifted Politician and Bard], I can [use Performance in place of Persuasion as long as I tell a story].
Finally, I'm tempted to say PCs get a number of stunts equal to their proficiency bonus, and can change an existing stunt everytime their bonus goes up. Maybe write up a feat that grants two bonus stunts.
Now, admittedly, some of these "Stunts" I'd just allow as a DM, but that doesn't mean I don't think having something like this gives some agency to players.