  We present a sample of 12 Quasi-Stellar Objects (QSOs) potentially acting as
strong gravitational lenses on background Emission Line Galaxies (ELG) or
Lyman-$\alpha$ Emitters (LAEs) selected selected through a systematic search of
the 297301 QSOs in the Sloan Digital Sky Survey (SDSS)-III Data Release 12.
Candidates are 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, 9 have definite evidence for the presence of a background ELG
identified by at least 4 higher-redshift nebular emission lines. The remaining
$3$ probable candidates present a strong asymmetrical emission line attributed
to a background Lyman-$\alpha$ emitter (LAE). The QSO-ELG (QSO-LAE) lens
candidates have QSO lens redshifts in the range $0.24\lesssim z_{QSO} \lesssim
0.66$ ($0.75 \lesssim z_{QSO} \lesssim 1.23$ ) and background galaxy redshifts
in the range $0.48 \lesssim z_{S,ELG} \lesssim 0.94$ ($2.17 \lesssim z_{S,LAE}
\lesssim 4.48$). 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. (Abridged)
