Simultaneous absorption of two photons has gained increasing attention over recent years as it opens the way for improved and novel technological capabilities. In the search for adequate materials that combine large two-photon absorption (TPA) responses and attributes suitable for specific applications, the multibranch strategy has proved to be efficient. Such molecular engineering effort, based on the gathering of several molecular units, has benefited from various theoretical approaches. Among those, the Frenkel exciton model has been shown to often provide a valuable qualitative tool to connect the optical properties of a multibranched chromophore to those of its monomeric counterpart. In addition, recent extensions of time-dependent density functional theory (TD-DFT) based on hybrid functionals have shown excellent performance for the determination of nonlinear optical (NLO) responses of conjugated organic chromophores and various substituted branched structures. In this paper, we use these theoretical approaches to investigate the one- and two-photon properties of triazole-based chromophores. In fact, experimental data were shown to reveal quite different behaviors as compared to related quadrupolar and octupolar compounds. Our theoretical findings allow elucidating these differences and contribute to the general understanding of structure-property relations. This work opens new perspectives towards synergic TPA architectures.