APOGEE spectra offer ~1 km s^-1 precision in the measurement of stellar radial velocities (RVs). This holds even when multiple stars are captured in the same spectrum, as happens most commonly with double-lined spectroscopic binaries (SB2s), although random line of sight alignments of unrelated stars can also occur. We develop a code that autonomously identifies SB2s and higher order multiples in the APOGEE spectra, resulting in 7273 candidate SB2s, 813 SB3s, and 19 SB4s. We estimate the mass ratios of binaries, and for a subset of these systems with sufficient number of measurements we perform a complete orbital fit, confirming that most systems with period <10 days have circularized. Overall, we find a SB2 fraction F_SB2~3% among main sequence dwarfs, and that there is not a significant trend in F_SB2 with temperature of a star. We are also able to recover a higher F_SB2 in sources with lower metallicity, however there are some observational biases. We also examine light curves from TESS to determine which of these spectroscopic binaries are also eclipsing. Such systems, particularly those that are also pre- and post-main sequence, are good candidates for a follow-up analysis to determine their masses and temperatures.