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I have used high-precision photometry and astrometry from the third data release of Gaia (DR3) to identify candidate members of the 32 Ori association. Spectral types and radial velocities have been measured for subsets of the candidates using new and archival spectra. For the candidates that have radial velocity measurements, I have used UVW velocities to further constrain their membership, arriving at a final catalog of 169 candidates. I estimate that the completeness of the survey is ~90% for spectral types of <=M7 (>=0.06 Msun). The histogram of spectral types for the 32 Ori candidates exhibits a maximum at M5 (~0.15 Msun), resembling the distributions measured for other young clusters and associations in the solar neighborhood. The available UVW velocities indicate that the association is expanding, but they do not produce a well-defined kinematic age. Based on their sequences of low-mass stars in color-magnitude diagrams, the 32 Ori association and Upper Centaurus-Lupus/Lower Centaurus-Crux (UCL/LCC) are coeval to within +/-1.2 Myr, and they are younger than the Beta Pic moving group by ~3 Myr, which agrees with results from previous analysis based on the second data release of Gaia. Finally, I have used mid-infrared (IR) photometry from the Wide-field Infrared Survey Explorer to check for excess emission from circumstellar disks among the 32 Ori candidates. Disks are detected for 18 candidates, half of which are reported for the first time in this work. The fraction of candidates at <=M6 that have full, transitional, or evolved disks is 10/149=0.07+0.03/-0.02, which is consistent with the value for UCL/LCC.