In this work, using the quadratic response theory and two-state model approach, we have explained the origin of high two-photon activity and the corresponding solvent dependence of 4,4'-dimethyl-amino-nitro-stilbene (DANS) molecule. For this purpose, we have made two structural modifications in the DANS molecule (1) at the donor acceptor part and (2) at the unsaturated bridge between the two rings and calculated the one- and two-photon (OP and TP) absorption parameters of all the systems in gas phase and in three different solvents, viz., MeCN, THF, and toluene. We found that the removal of donor acceptor groups from the original DANS molecule vanishes the transition moment between the ground and excited states and also the corresponding dipole moment difference, and the saturation of the pi-conjugation bridge between the two rings keeping the donor acceptor groups intact causes a large decrease in the ground to excited state transition moment. These changes, in turn, decrease the overall TP activity of the molecules as compared to DANS. On the basis of our analysis, we have concluded that neither the donor acceptor pair nor the pi-conjugation bridge between the two, rather their cooperative involvement leads to a large overlap between the ground and virtual and also the virtual and charge-transfer states, which are eventually responsible for the very large TP activity of DANS.