  We study a unitary matrix model of the Gross-Witten-Wadia type, extended with
the addition of characteristic polynomial insertions. The model interpolates
between solvable unitary matrix models and is the unitary counterpart of a
deformed Cauchy ensemble. Exact formulas for the partition function and Wilson
loops are given in terms of Toeplitz determinants and minors and large $N$
results are obtained by using Szeg\"o theorem with a Fisher-Hartwig
singularity. In the large $N$ (planar) limit with two scaled couplings, the
theory exhibits a surprisingly intricate phase structure in the two-dimensional
parameter space.
