High precision proper motions are currently available for approximately 20% of the Milky Way's known satellite galaxies. Often, the 6D phase space information of each satellite is used separately to constrain the mass of the MW. In this talk, I will discuss the Bayesian framework outlined in Patel et al. 2017b to make inferences of the MW's mass using satellite properties such as specific orbital angular momentum, rather than just position and velocity. By extending this framework from one satellite to a population of satellites, we can now form simultaneous MW mass estimates using the Illustris-Dark cosmological simulation that are unbiased by high speed satellites such as Leo I (Patel et al., submitted). Our resulting MW mass estimates reduce the current factor of two uncertainty in the mass range of the MW and show promising signs for improvement as upcoming ground- and space-based observatories obtain proper motions for additional MW satellite galaxies.