NASA’s TESS mission will eventually find hundreds of small planets orbiting small stars, many of which will reside in multi-planet systems. Determination of the density of many of these TESS planets will rely upon follow-up radial velocity campaigns—yet, this radial velocity data will encode both non-transiting and transiting planets (including transiting planets lurking below TESS’ sensitivity threshold). Many of these unseen additional planets will contribute to the RV signature at around the m/s level, where they have an effect on our interpretation of the radial velocity curves despite remaining undetected. We present the results of an investigation into the predicted effect that undetected planets will have on detected TESS planet mass measurements, folding together expected demographics of planetary systems orbiting M dwarfs with simulated radial velocity observations. Existing knowledge about the architectures of multi-planet systems orbiting M dwarfs allows us to apply an informative prior on the expected radial velocity observations.