We study two-photon absorption (2PA) in two series of new free-base porphyrins with 4-(diphenylamino)stilbene or 4,4'-bis-(diphenylamino)stilbene (BDPAS) attached via pi-conjugating linkers at the porphyrin meso-position. We show that this new substitution modality increases the 2PA cross section in the Soret band region (excitation wavelength 750-900 nm) of the core porphyrin by nearly 2 orders of magnitude, from sigma(2) approximately 10 GM for the meso-phenyl-substituted analogue to sigma(2) approximately 10(3) GM for the ethynyl-linked BDPAS-porphyrin dyad. The 2PA properties are quantitatively described by considering two different and interfering 2PA quantum transition pathways. The first path involves virtual transition via intermediate one-photon resonance. The second path bypasses the intermediate resonance and occurs due to a large permanent dipole moment difference between the ground and the final electronic states. To our best knowledge, this is the first experimental observation of the combined effect of these two pathways on one particular two-photon transition, resulting in quantum-interference-modulated 2PA strength.