  Large cavities are often observed in protoplanetary disks, which might
suggest the presence of planets opening gaps in the disk. Multiple planets are
necessary to produce a wide cavity in the gas. However, multiple planets may
also be a burden to the carving out of very deep gaps. When additional planets
are added to the system, the time-dependent perturbations from these additional
satellites can stir up gas in the gap, suppressing cavity opening. In this
study, we perform two-dimensional numerical hydro calculations of gap opening
for single and multiple planets, showing the effect that additional planets
have on the gap depths. We show that multiple planets produce much shallower
cavities than single planets, so that more massive planets are needed in the
multiple-planet case to produce an equivalent gap depth as in the single-planet
case. To deplete a gap by a factor of 100 for the parameters chosen in this
study, one only requires $M_p \approx 3.5M_J$ in the single-planet case, but
much more massive planets, $M_p \approx 7M_J$ are required in the
multiple-planet case. This requirement of high-mass planets implies that such
planets may be detectable in the next generation of direct imaging projects, in
gaps whose depths are constrained to be sufficiently deep by ALMA.
