Shaska [@CMSE7] extended the construction of non-geometric heterotic strings by Malmendier and Morrison to non-geometric heterotic strings with unbroken $\mathfrak{e}_7\mathfrak{e}_7$ algebra. F-theory compactifications on elliptic K3 surfaces with $H\oplus E_7\oplus E_7$ lattice polarization, namely K3 surfaces with a global section with two type $III^*$ fibers, were considered, and eight-dimensional non-geometric heterotic strings on $T^2$ were obtained as the heterotic duals in their construction. The moduli of the resulting heterotic strings is parametrized by the space $$D_{2,4} / O^+(L^{2,4}).$$ Here $D_{2,4}$ is the symmetric space of $O(2,4)$, namely, $D_{2,4}$ is defined as $O(2)\times O(4)\backslash O(2,4)$. The symmetric space $D_{2,4}$ is also referred to as the [*bounded symmetric domain of type $IV$*]{}. Here $L^{2,4}$ denotes the orthogonal complement of $H\oplus E_7\oplus E_7$ in the K3 lattice $\Lambda_{K3}$. The complex structure moduli, Kähler moduli, and the moduli of Wilson line expectation values are mixed under the symmetry $O^+(L^{2,4})$, thus the heterotic strings constructed in [@CMSE7] also do not have a geometric interpretation. Two Wilson line expectation values are non-trivial in non-geometric heterotic strings with unbroken $\mathfrak{e}_7\mathfrak{e}_7$ algebra. See also [@GJ1412; @LMV1508; @FGLMM1603; @MS1609; @GLMM1611; @FM1708; @FGLMM1712; @Kimura1810; @Plauschinn2018] for recent progress on non-geometric heterotic strings.

In this note, we analyze theories that correspond 