  Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized
in optical systems, accurately model the properties of open, bosonic systems
with balanced, spatially separated gain and loss. We present a family of
exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a
non-relativistic particle confined in a circular geometry. We show that the
$\mathcal{PT}$ symmetry threshold can be tuned by introducing a second
gain-loss potential or its hermitian counterpart. Our results explicitly
demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase
diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.
