The two-photon absorption (TPA) properties of two extended symmetric squaraine dyes are thoroughly characterized from the experimental and quantum-chemical point of view. The two molecules are specially engineered to have a multipolar structure with increasing complexity, D-pi-A-pi-D and A'-pi-D-pi-A-pi-D-pi-A', respectively. The experimental TPA spectra, measured by means of the Z-scan technique in the femtoseconds regime, display considerably high values of TPA cross sections (sigma(TPA)) for both molecules. In particular, the squaraine with the more extended structure shows the highest value of sigma(TPA) ever reported for this class of molecules. CIS and TDDFT calculations of the one and two-photon absorption properties are carried out to clarify the origin of the observed TPA properties and fully characterize the electronic properties of these compounds. The calculations, in good agreement with the experimental data, suggest that the origin of this exceptionally high sigma(TPA) can be ascribed to the presence of a peripheral A' group, that increases the density of excited states involved in the TPA process.