  We test the refined distance conjecture in the vector multiplet moduli space
of 4D $\mathcal{N}=2$ compactifications of the type IIA string that admit a
dual heterotic description. In the weakly coupled regime of the heterotic
string, the moduli space geometry is governed by the perturbative heterotic
dualities, which allows for exact computations. This is reflected in the type
IIA frame through the existence of a K3 fibration. We identify the degree
$d=2N$ of the K3 fiber as a parameter that could potentially lead to large
distances, which is substantiated by studying several explicit models. The
moduli space geometry degenerates into the modular curve for the congruence
subgroup $\Gamma_0(N)^+$. In order to probe the large $N$ regime, we initiate
the study of Calabi-Yau threefolds fibered by general degree $d>8$ K3 surfaces
by suggesting a construction as complete intersections in Grassmann bundles.
