  We propose an organizing principle for string theory moduli spaces in six
dimensions with $\mathcal{N} = (1,1)$, based on a rank reduction map, into
which all known constructions fit. In the case of cyclic orbifolds, which are
the main focus of the paper, we make an explicit connection with meromorphic 2D
(s)CFTs with $c = 24$ ($c = 12$) and show how these encode every possible gauge
symmetry enhancement in their associated 6D theories. These results generalize
naturally to non-cyclic orbifolds, into which the only known string
construction (to our awareness) also fits. This framework suggests the
existence of a total of 47 moduli spaces: the Narain moduli space, 23 of cyclic
orbifold type and 23 of non-cyclic type. Of these only 17 have known string
constructions. Among the 30 new moduli spaces, 15 correspond to pure
supergravity, for a total of 16 such spaces. A full classification of
nonabelian gauge symmetries is given, and as a byproduct we complete the one
for seven dimensions, in which only those of theories with heterotic
descriptions were known exhaustively.
