Sensitive radio continuum data could bring the number of known supernova remnants (SNRs) in the Galaxy more in line with what is expected. Due to confusion in the Galactic plane, however, faint SNRs can be challenging to distinguish from brighter HII regions and filamentary radio emission. We exploited new 1.3GHz SARAO MeerKAT Galactic Plane Survey (SMGPS) radio continuum data, which cover 251{deg}<l<358{deg} and 2{deg}<l<61{deg} at |b|<1.5{deg}, to search for SNR candidates in the Milky Way disk. We also used mid-infrared data from the Spitzer GLIMPSE, Spitzer MIPSGAL, and WISE surveys to help identify SNR candidates. These candidates are sources of extended radio continuum emission that lack mid-infrared counterparts, are not known as HII regions in the WISE Catalog of Galactic HII Regions, and have not been previously identified as SNRs. We locate 237 new Galactic SNR candidates in the SMGPS data. We also identify and confirm the expected radio morphology for 201 objects classified in the literature as SNRs and 130 previously identified SNR candidates. The known and candidate SNRs have similar spatial distributions and angular sizes. The SMGPS data allowed us to identify a large population of SNR candidates that can be confirmed as true SNRs using radio polarization measurements or by deriving radio spectral indices. If the 237 candidates are confirmed as true SNRs, it would approximately double the number of known Galactic SNRs in the survey area, alleviating much of the discrepancy between the known and expected populations.