We present a catalog of 97 uniformly vetted candidates for quadruple star systems. The candidates were identified in TESS full-frame image data from sectors 1-42 through a combination of machine-learning techniques and visual examination, with major contributions from a dedicated group of citizen scientists. All targets exhibit two sets of eclipses with two different periods, both of which pass photocenter tests confirming that the eclipses are on target. This catalog outlines the statistical properties of the sample, nearly doubles the number of known multiply eclipsing quadruple systems, and provides the basis for detailed future studies of individual systems. Several important discoveries have already resulted from this effort, including the first sextuply eclipsing sextuple stellar system and the first transiting circumbinary planet detected from one sector of TESS data.