  Two-dimensional $\sigma$-models corresponding to coset CFTs of the type $
(\hat{\mathfrak{g}}_k\oplus \hat{\mathfrak{h}}_\ell )/
\hat{\mathfrak{h}}_{k+\ell}$ admit a zoom-in limit involving sending one of the
levels, say $\ell$, to infinity. The result is the non-Abelian T-dual of the
WZW model for the algebra $\hat{\mathfrak{g}}_k$ with respect to the vector
action of the subalgebra $\mathfrak{h}$ of $ \mathfrak{g}$. We examine modular
invariant partition functions in this context. Focusing on the case with
$\mathfrak{g}=\mathfrak{h}=\mathfrak{su}(2)$ we apply the above limit to the
branching functions and modular invariant partition function of the coset CFT,
which as a whole is a delicate procedure. Our main concrete result is that such
a limit is well defined and the resulting partition function is modular
invariant.
