Flag-transitive extensions of Cn geometries

We consider locally C(n)-geometries where all planes are circular spaces (i.e., complete graphs). We call them extensions of C(n)-geometries or (c.C(n)) geometries, for short. We give a classification of finite flag-transitive (c.C(n)) geometries when n greater-than-or-equal-to 3. A classification is given also in the case of n = 2 under the hypothesis that residues of points are thick classical generalized quadrangles.