Exoplanet systems with multiple transiting planets are natural laboratories for testing planetary astrophysics. One such system is HD191939 (TOI1339), 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 38days each with similar sizes from 3 to 3.4R{Earth}. To further characterize the system, we measured the radial velocity (RV) of HD191939 over 415days with Keck/HIRES and APF/Levy. We find that M_b_=10.4{+/-}0.9M{Earth} and M_c_=7.2{+/-}1.4M{Earth}, which are low compared to most known planets of comparable radii. The RVs yield only an upper limit on M_d_ (<5.8M{Earth} at 2{sigma}). The RVs further reveal a fourth planet (e) with a minimum mass of 0.34{+/-}0.01M_Jup_ and an orbital period of 101.4{+/-}0.4days. Despite its nontransiting geometry, secular interactions between planet e and the inner transiting planets indicate that planet e is coplanar with the transiting planets ({Delta}i<10{deg}). We identify a second high-mass planet (f) with 95% confidence intervals on mass between 2 and 11M_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, HD191939 presents many options for comparative planetary astronomy, including characterization with JWST.