That depends entirely on how it's structured. For example if you know how long a particular check will take then an obvious upgrade to that skill is to make that time shorter. If you know the range, then make the range longer. As long as the system has more detail than zero, then it's always possible to improve them.Pathfinder has explored this. Pathfinder Unchained introduced skill unlocks, which lets you do new things with skills as you gain proficiency ranks. Pathfinder 2e goes a different direction with skill feats. Do they do what you propose? Well, that’s the problem.
If you treat them as unlocking new capabilities, then the implication is you cannot even attempt them without the appropriate capability. It’s like how there is no way to cast delayed blast fireball when all you know is the fireball spell. If you don’t have the appropriate no-tools ability, then you cannot pick locks without tools. The problem is that’s not how people want to use skills. You see this criticism levied at PF2.
A bunch of my examples even ignore rolls entirely. Look at my example post with movement speeds in them. You could make a movement related skill that, as you advance it, you move faster, become a better swimmer, become a better climber.
Skill feats are kinda what I'm after, but I feel their implementation is a bit too complicated and niche.
Yes kinda. The problem I see with skill feats is that they are still quite separate from the skill system. I think for me they feel a bit tacked on. The system is still based on checks and modifiersThe response typically is to point out that skill feats are allowing you to do something at a reduced cost. The activity takes less time, you can perform it at a reduced DC, or it might allow you to get more out of your roll. I think that’s a good approach for Pathfinder, but is that what you want? It doesn’t seem like it. I’m not sure this is really solvable in a D&D-like game without making major changes to how skills work and are used by the system.