We study three-photon absorption (3PA) in a series of 4,4'-bis(diphenylamino) stilbene-based dendrimers and show that the cross section of the nonlinear absorption scales faster than in a linear fashion with the molecular size, which is a manifestation of the cooperative enhancement effect. The coherent domain structure is deduced from 3PA cross section values for all of the dendrimers in the series. It is found that, in terms of largest coherence domain size, the optimum dendrimer generation is 4-arm G-0. Molecular 3PA cross section, sigma(3) = 10(-79) cm(6) s(2), is obtained for 4-arm G-2 dendrimer generation, which is, to our best knowledge, one of the largest intrinsic sigma(3) values measured for any organic molecule.