Aims. We continue our investigation of the bulk properties of asteroid dynamical families identified using only asteroid proper elements to provide plausible collisional interpretations. We focus on cratering families consisting of a substantial parent body and many small fragments. Methods. We propose a quantitative definition of cratering families based on the fraction in volume of the fragments with respect to the parent body; fragmentation families are above this empirical boundary. We assess the compositional homogeneity of the families and their shape in proper element space by computing the differences of the proper elements of the fragments with respect to the ones of the major body, looking for anomalous asymmetries produced either by post-formation dynamical evolution, or by multiple collisional/cratering events, or by a failure of the hierarchical clustering method (HCM) for family identification. Results. We identified a total of 25 dynamical families with more than 100 members ranging from moderate to heavy cratering. For three families (4, 15 and 283) we confirm the occurrence of two separate cratering events, while family (569) Misa is a mixed case, with one cratering event and one fragmentation event. The case of family 3 remains dubious, in that there could be either one or two collisions. For family 20, we propose a double collision origin, not previously identified. In four cases (31, 480, 163 and 179) we performed a dedicated search for dynamical resonant transport mechanisms that could have substantially changed the shape of the family. By using a new synthetic method for computation of secular frequencies, we found possible solutions for families 31, 480, and 163, but not for family 179, for which we propose a new interpretation, based on a secular resonance contaminating this family: the family of 179 should be split into two separate clusters, one containing (179) itself and the other, family (9506) Telramund, of fragmentation type, for which we have computed an age.