A comprehensive understanding of the influence of the different structural elements for the molecular properties is crucial for improving the material design procedures in the field of photosensitive dyes. The present study provides a detailed analysis of the influence of the number of heteroatoms (nitrogens) and the lengths of the pi-electron skeleton on the one- and two-photon absorption of the symmetric squaraine dyes. Extended computational study covers the conventional vertical excitation calculations within the TD-DFT formalisms as well as several advanced single-reference methods including double excitations such as CIS(D), SAC-CI, and ADC(2). Additionally, the weaknesses of the vertical approach are investigated by including the geometry relaxation upon excitation via adiabatic and 0-0 treatment.