Offer more choice in build and action in regards to the ability check side of gameplay.
That's just a way to rephrase "I want more complex checks."
This is like asking, "What would a more complex spaghetti and meatballs recipe look like?" Well, what problem are you trying to solve? Saying, "Well I want it to have more flavors," doesn't explain anything. You've got to be able to explain what's wrong and why you think your recipe needs improvement.
The question is: What
gameplay problem are you trying to solve by changing the game? What is your design
goal? How can you tell if your change is better if you don't know why you'd make the change? You can't really begin to make game design choices about potential solutions until you have stated the problem that you're trying to fix as clearly as you can.
For example, let's say you change every skill check to require a die roll and looking up the result on a table. No matter how simple the check, you have to make a die roll and reference a table. That's more complex. Can we stop designing there? Does that solve the problem? How do we know? Do we need to make skill checks like rolling for treasure hoards? Rolling twelve times on six different tables? Do we need to have a 300 page book just about skills and skill checks? Is that
too complex? How do we know?
A little board because I don't want to narrow in on an answer before I get the question, but DnD doesn't have a lot of mechanical hooks if you want to invest in skills.
Yeah, but you've already decided on the solution: make skill checks more complex. What we don't understand is
why that's your solution. We want to know not just how you arrived as "increase complexity" as your solution, but what prompted you to improve the game in the first place.
What do you mean by "mechanical hook"? What does the game currently do? What does the game fail to do that you think it should do?
It feels like you're asking people to brainstorm designs that are more complex and then you'll evaluate them to see if you like them better. That's like making a better spaghetti and meatballs by asking everyone else to make a new recipe and then tasting every single one and then picking one.