At present a special attention is concentrated on increasing of the efficiency of multi-photon absorption of organic systems because of new emerging applications based on this effect. In our experiments we use strong two-photon absorbing chromophore, 4,4’-bis(diphenylamino)stilbene (BDPAS), to design new dendrimer molecules, in such a way that the branching center allows for pi-electronic conjugation between branches. Here we present, for the first time, unambiguous spectroscopic evidence of strong cooperative enhancement of two-photon and three-photon absorption in a series of these dendritic macromolecules. Maximum two-photon cross section increases in proportion to N2, where N = 2, 4, 6 is the number of constituent identical chromophore units in the parent BDPAS and lowest, G-0 dendrimer generation. Almost the same scaling law is observed for three-photon absorption. For higher generations, G-1 and G-2, comprising N = 14 and 30 chromophores, respectively, the cooperativity in multiphoton response starts to saturate. We show that three-photon absorption provides important complementary information, which we use for evaluation of the size of domains where chromophores are coherently coupled.