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This paper presents a comprehensive analysis of four triply eclipsing triple star systems, namely TIC 88206187, TIC 14839347, TIC 298714297, and TIC 66893949. The four systems with third-body eclipses were found in the TESS light curves from among a sample of ∼400 matches between known eclipsing binaries and the Gaia DR3 Non-Single Star solution data base. We combined photometric light curves, eclipse timing variations, archival spectral energy distributions, and theoretical evolution tracks in a robust photodynamical analysis to determine the orbital and system parameters. The triples have outer periods of 52.9 d, 85.5 d, 117 d, and 471 d, respectively. All dozen stars have masses ≲ 2.6 M⊙. The systems are quite flat with mutual inclination angles between the inner and outer orbital planes that are all ≲ 4°. The outer mass ratios (q ≡ M 3/ M bin) range from 0.39 to 0.76, consistent with our earlier collection of compact triply eclipsing triples. TIC 88206187 exhibits a fractional radius of the outer tertiary component (r B ≡ R B / a out) exceeding 0.1 (only the third such system known), and we consider its future evolution. Finally, we compare our photodynamical analysis results and the orbital parameters given in the Gaia DR3 NSS solutions, indicating decent agreement, but with the photodynamical results being more accurate. [ABSTRACT FROM AUTHOR]