  A recent ALMA image revealed several concentric gaps in the protoplanetary
disk surrounding the young star HL Tau. We consider the hypothesis that these
gaps are carved by planets, and present a general framework for understanding
the dynamical stability of such systems over typical disk lifetimes, providing
estimates for the maximum planetary masses. We collect these easily evaluated
constraints into a workflow that can help guide the design and interpretation
of new observational campaigns and numerical simulations of gap opening in such
systems. We argue that the locations of resonances should be significantly
shifted in massive disks like HL Tau, and that theoretical uncertainties in the
exact offset, together with observational errors, imply a large uncertainty in
the dynamical state and stability in such disks. This presents an important
barrier to using systems like HL Tau as a proxy for the initial conditions
following planet formation. An important observational avenue to breaking this
degeneracy is to search for eccentric gaps, which could implicate resonantly
interacting planets. Unfortunately, massive disks like HL Tau should induce
swift pericenter precession that would smear out any such eccentric features of
planetary origin. This motivates pushing toward more typical, less massive
disks. For a nominal non-resonant model of the HL Tau system with five planets,
we find a maximum mass for the outer three bodies of approximately 2 Neptune
masses. In a resonant configuration, these planets can reach at least the mass
of Saturn. The inner two planets' masses are unconstrained by dynamical
stability arguments.
