When tensor products of N minimal models accumulate at central charge N, they also admit relevant operators arbitrarily close to marginality. This raises the tantalizing possibility that they can be use to reach purely Virasoro symmetric CFTs where the breaking of extended chiral symmetry can be seen in a controlled way. The main confirmation of this comes from a brute force computation of correlators involving UV currents and their would-be divergences. I will explain this check, which was first done for permutation invariant currents, along with lessons that have recently been learned by extending it to general currents. I will also discuss the non-invertible symmetries preserved by these models and some ideas for probing them more deeply with non-perturbative methods.