[Dulcimer Hall] Grafting two mechanics?

For my next design, I'm looking to create a game where two different activities have important rules support.

It will have an explicit system for letting players create facts, theories, lies, secrets and scandals, to move items from one category to the other, and to combine elements for increased potency.

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Example: In-game: "I didn't know what the footprints in the garden or the strange looks from Jason meant, but when I saw mud and crushed azaleas on his doormat I realized that he must have been standing at the window when I lied to Jackie about my feelings toward him... he must hate me!"

Rules (rough): "Okay, with the mud fact I've got a workable sequence. Using Footprints, Strange Look and Mud to shift Jason Saw It All from Secrets to my Known column. Now I'm using that, together with "Jason Confesses his Love" to create the theory "Jason Hates me" at level 2.

My issue is that this system is (as I see it) too focussed to deal with many of the things that I (as a player) want to do. A game where every action in every scene has to revolve around the transfer of information is too cerebral for my tastes.

So I also need a system to handle day-to-day things like climbing gantries, scamming extra pudding from the cafeteria ladies and acing your math mid-terms.

What I'm wondering about is whether there are good examples of games where people successfully graft two mechanics systems together, in ways that address two different goals, but which mutually support and inform each other. I'm not thinking of any off-hand, but that may well just be because once that grafting takes place it's hard to think of them as two systems.