Structurally related chromophores of different symmetry (dipolar, V-shaped, octupolar) are investigated and compared for elucidation of the combined role of branching and charge symmetry on absorption, photoluminescence and two-photon absorption (TPA). Their design is based on the assembly of one, two or three π-conjugated dipolar branches on a central core. Two series of branched structures obtained from a central triphenylamine core and dipolar branches having different charge-transfer characters are investigated: photophysical properties are studied and TPA spectra are determined through two-photon excited fluorescence experiments using fs pulses in the 700-1000 nm range. Calculations based on time-dependent quantum-chemical approaches, as well as the Frenkel exciton model, complement experimental findings. Experiments and theory reveal that a multidimensional intramolecular charge transfer takes place from the central electron-donating moiety to the periphery of the branched molecules upon excitation, whereas fluorescence stems from a dipolar branch. Symmetry and inter-branch electronic coupling are found to be responsible for amplification of the TPA response of branched compounds with respect to their monomeric analogues. In particular, an enhancement is observed in regions where the TPA bands overlap, and TPA activation is obtained in spectral regions where the dipolar analogue is almost two-photon transparent. Thus, appropriate tuning of the number of branches, of the coupling between them, and modulation of intramolecular charge transfer from core to periphery open the way for substantial improvement of TPA efficiency or TPA induction in desired spectral regions.