Abstract Exoplanet systems with multiple transiting planets are natural laboratories for testing planetary astrophysics. One such system is HD 191939 (TOI 1339), a bright (V = 9) and Sun-like (G9V) star, which TESS found to host three transiting planets (b, c, and d). The planets have periods of 9, 29, and 38 days each with similar sizes from 3 to 3.4 R _⊕. To further characterize the system, we measured the radial velocity (RV) of HD 191939 over 415 days with Keck/HIRES and APF/Levy. We find that M _b = 10.4 ± 0.9 M _⊕ and M _c = 7.2 ± 1.4 M _⊕, which are low compared to most known planets of comparable radii. The RVs yield only an upper limit on M _d (<5.8 M _⊕ at 2σ). The RVs further reveal a fourth planet (e) with a minimum mass of 0.34 ± 0.01 M _Jup and an orbital period of 101.4 ± 0.4 days. Despite its nontransiting geometry, secular interactions between planet e and the inner transiting planets indicate that planet e is coplanar with the transiting planets (Δi < 10°). We identify a second high-mass planet (f) with 95% confidence intervals on mass between 2 and 11 M _Jup and period between 1700 and 7200 days, based on a joint analysis of RVs and astrometry from Gaia and Hipparcos. As a bright star hosting multiple planets with well-measured masses, HD 191939 presents many options for comparative planetary astronomy, including characterization with JWST.