We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is self-dual under the gauge transformation. The critical properties of the model are studied numerically with the Corner Transfer Matrix Renormalization Group method. Accuracy of the method is tested on two exactly solvable cases: the Ising model and a specific version of the Baxter eight-vertex model in a zero field that belong to different universality classes. Numerical results show that the two exactly solvable cases are connected by a line of critical points with the polarization as the order parameter. There are numerical indications that critical exponents vary continuously along this line in such a way that the weak universality hypothesis is violated.
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