We present a sample of 12 quasi-stellar objects (QSOs) that potentially act as strong gravitational lenses on background emission line galaxies (ELG) or Lyman- α emitters (LAEs) selected through a systematic search of the 297 301 QSOs in the Sloan Digital Sky Survey (SDSS)-III Data Release 12. Candidates were identified by looking for compound spectra, where emission lines at a redshift larger than that of the quasar can be identified in the residuals after a QSO spectral template is subtracted from the observed spectra. The narrow diameter of BOSS fibers (2″) then ensures that the object responsible for the additional emission lines must lie close to the line of sight of the QSO and hence provides a high probability of lensing. Among the 12 candidates identified, nine have definite evidence for the presence of a background ELG identified by at least four higher-redshift nebular emission lines. The remaining three probable candidates present a strong asymmetrical emission line attributed to a background Lyman- α emitter (LAE). The QSO-ELG (QSO-LAE) lens candidates have QSO lens redshifts in the range 0.24 ≲  z _QSO  ≲ 0.66 (0.75 ≲  z _QSO  ≲ 1.23 ) and background galaxy redshifts in the range 0.48 ≲  z _S, ELG  ≲ 0.94 (2.17 ≲  z _S, LAE  ≲ 4.48). We show that the algorithmic search is complete at > 90% for QSO-ELG systems, whereas it falls at 40−60% for QSO-LAE, depending on the redshift of the source. Upon confirmation of the lensing nature of the systems, this sample may quadruple the number of known QSOs acting as strong lenses. We have determined the completeness of our search, which allows future studies to compute lensing probabilities of galaxies by QSOs and differentiate between different QSO models. Future imaging of the full sample and lens modelling offers a unique approach to study and constrain key properties of QSOs.