  Limits of families of conformal field theories are of interest in the context
of AdS/CFT dualities. We explore here the large level limit of the
two-dimensional N=(2,2) superconformal W_{n+1} minimal models that appear in
the context of the supersymmetric higher-spin AdS3/CFT2 duality. These models
are constructed as Kazama-Suzuki coset models of the form SU(n+1)/U(n). We
determine a family of boundary conditions in the limit theories, and use the
modular bootstrap to obtain the full bulk spectrum of N=2 super-W_{n+1}
primaries in the theory. We also confirm the identification of this limit
theory as the continuous orbifold C^n/U(n) that was discussed recently.
