The current sample of 12 radio-quiet isolated neutron stars that emit strongly in X-rays (XINSs) is both small and heterogeneous, limiting its usefulness for understanding the physics of neutron star atmospheres and cooling rates and for constraining the equation of state of neutron degenerate matter. Utilizing the ROSAT 1RXS and 2RXS data sets, in conjunction with the Sloan Digital Sky Survey Data Release 17 and other companion multiwavelength surveys, we have extended previous searches for blank-field X-ray source candidate XINSs, ultimately recovering two known XINSs while identifying 46 new, unstudied candidate fields devoid of likely multiwavelength counterparts. In this publication, we describe our selection approach and provide detailed information regarding our sample of new candidate XINSs. Future opportunities to verify or to refute these X-ray sources as isolated neutron stars by obtaining more accurate X-ray source positions, quality X-ray spectra, or deeper optical imaging are also discussed.