  We present the experimental discovery of multiple simultaneous degeneracies
in the spectrum of a Kerr oscillator subjected to a squeezing drive. This
squeezing, in combination with the Kerr interaction creates an effective static
two-well potential in the frame rotating at half the frequency of the
sinusoidal driving force. Remarkably, these degeneracies can be turned
on-and-off on demand, and their number is tunable. We find that when the
detuning $\Delta$ between the frequency of the oscillator and characteristic
frequency of the drive equals an even multiple of the Kerr coefficient $K$,
$\Delta/K = 2m$, the oscillator displays $m + 1$ exact, parity-protected,
spectral degeneracies, insensitive to the drive amplitude. The degeneracies
stem from the unusual destructive interference of tunnel paths in the
classically forbidden region of the double well static effective potential that
models our experiment. Exploiting this interference, we measure a peaked
enhancement of the incoherent well-switching lifetime creating a
super-protected cat qubit in the ground state manifold of our oscillator. {Our
results demonstrate the relationship between degeneracies and noise protection
in quantum systems.
