Makkai's suggestion

In "Towards a categorical foundation of mathematics", Makkai wrote that: "This suggests that, possibly, the right approach to the definition of weak n-category is to aim at formulating all coherence conditions at once, regardless the fact that this might give a very "theoretical" definition. It would then be a separate, and still very important, project to find a (hopefully) finite and concise set of coherence conditions that would be enough to imply all coherence conditions." It was 15 years ago! Did this approach give something? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]