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Shed Skin may be something worth considering: it's bad for DD, since those sets value burn immunity a lot and usually start sweeping after a boost, so waiting for the ability to remove status is not good; CM sets are slower to build up boosts and may be more likely to pack recovery of some sort...
I would be very careful considering Sheer Force for this CAP. It gives insane power right off the bat, which means a mixed set looks more appealing. I guess we could scale down every single attacking stat to obtain acceptable levels of power when unboosted, but you'd immediately kill the...
I have a hard time seeing how we can build CAP around Agility / RP + something else. An Agility set would require good attacking power (obviously), but also better than average bulk, at least physically (since the tier is littered with priority), and still cannot afford to have awful Speed...