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The example that I had in mind was advancing the throttles to full, with the mixture still set at a sensible LOP setting
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Lycoming got it right on their full controller. When one advances the throttle when LOP, the mixture gets LEANER--exactly what we want to happen. Since no one set LOP could effectively advance the throttle to WOT as on takeoff, any enrichment feature is moot. The engine as set up will not run LOP above about 33" MP, so fuel enrichment is not an operational issue. We have tried to define why most of the engines will not run smoothly above about 32-33"MP LOP. (The exception being the GTSIO engines which runs smoothly LOP up to about 36" MP.) We have come up with some pretty good theories, all of which when tested, were wrong. (I hate when that happens)
Lycoming said the opposite--that the mixture got richer when the throttle was advanced. When we told them that's not how their how their fuel controller worked, they insisted that it did the opposite. We sent them the DATA on the TIO-540-J2BD from the test stand and they now agree that when the throttle is advanced from a LOP setting, that the mixture gets leaner--as it should.
Some fuel enrichment features are accomplished with an extra jet, others with a cam arrangement. As Jabba said, "it depends on the controller."