  We investigate the effects of competition between two complex,
$\mathcal{PT}$-symmetric potentials on the $\mathcal{PT}$-symmetric phase of a
"particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and
$V_\xi(x)=i\xi[\delta(x-a)-\delta(x+a)]$, represent long-range and localized
gain/loss regions respectively. We obtain the $\mathcal{PT}$-symmetric phase in
the $(Z,\xi)$ plane, and find that for locations $\pm a$ near the edge of the
box, the $\mathcal{PT}$-symmetric phase is strengthened by additional losses to
the loss region. We also predict that a broken $\mathcal{PT}$-symmetry will be
restored by increasing the strength $\xi$ of the localized potential. By
comparing the results for this problem and its lattice counterpart, we show
that a robust $\mathcal{PT}$-symmetric phase in the continuum is consistent
with the fragile phase on the lattice. Our results demonstrate that systems
with multiple, $\mathcal{PT}$-symmetric potentials show unique, unexpected
properties.
