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We present a radial velocity (RV) analysis of TOI-1136, a bright TESS systemwith six confirmed transiting planets, and a seventh single-transiting planetcandidate. All planets in the system are amenable to transmission spectroscopy,making TOI-1136 one of the best targets for intra-system comparison ofexoplanet atmospheres. TOI-1136 is young ($\sim$ 700 Myr), and the systemexhibits transit timing variations (TTVs). The youth of the system contributesto high stellar variability on the order of 50 m s$^{-1}$, much larger than thelikely RV amplitude of any of the transiting exoplanets. Utilizing 359 HIRESand APF RVs collected as a part of the TESS-Keck Survey (TKS), and 51 HARPS-NRVs, we experiment with a joint TTV-RV fit. With seven possible transitingplanets, TTVs, more than 400 RVs, and a stellar activity model, we posit thatwe may be presenting the most complex mass recovery of an exoplanet system inthe literature to date. By combining TTVs and RVs, we minimized GP overfittingand retrieved new masses for this system: (m$_{b-g}$ = 3.50$^{+0.8}_{-0.7}$,6.32$^{+1.1}_{-1.3}$, 8.35$^{+1.8}_{-1.6}$, 6.07$^{+1.09}_{-1.01}$,9.7$^{+3.9}_{-3.7}$, 5.6$^{+4.1}_{-3.2}$ M$_{\oplus}$). We are unable tosignificantly detect the mass of the seventh planet candidate in the RVs, butwe are able to loosely constrain a possible orbital period near 80 days. FutureTESS observations might confirm the existence of a seventh planet in thesystem, better constrain the masses and orbital properties of the knownexoplanets, and generally shine light on this scientifically interestingsystem.

The TESS-Keck Survey XVII: Precise Mass Measurements in a Young, High  Multiplicity Transiting Planet System using Radial Velocities and Transit  Timing Variations