The latest Gaia data release enables us to accurately identify stars that are more luminous than would be expected on the basis of their spectral type and distance. During an investigation of the 329 best solar twin candidates uncovered among the spectra acquired by the GALAH survey, we identified 64 such overluminous stars. In order to investigate their exact composition, we developed a data-driven methodology that can generate a synthetic photometric signature and spectrum of a single star. By combining multiple such synthetic stars into an unresolved binary or triple system and comparing the results to the actual photometric and spectroscopic observations, we uncovered 6 definitive triple stellar system candidate and an additional 14 potential candidates whose combined spectrum mimics the solar spectrum. Considering the volume correction factor for a magnitude-limited survey, the fraction of probable unresolved triple stars with long orbital periods is 2 per cent. Possible orbital configurations of the candidates were investigated using the selection and observational limits. To validate the discovered multiplicity fraction, the same procedure was used to evaluate the multiplicity fraction of other stellar types.