I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known.

Are there such?

Aren't minimal models supposed to have this property?

Even if not exactly known, can the n-point functions (may be when written as a conformal block expansion) be written order-by-order as a power series in the central charge? (..I guess there is some theorem about the asymptotic exponential dependence of the conformal blocks on the central charge (reference help? ) and I want to know if 1/c corrections to that are known..)