  Theories formulated in the arena of teleparallel geometries are generically
plagued by ghost-like instabilities or other pathologies that are ultimately
caused by the breaking of some symmetries. In this work, we construct a class
of ghost-free theories based on a symmetry under Transverse Diffeomorphisms
that is naturally realised in symmetric teleparallelism. We explicitly show
their equivalence to a family of theories with an extra scalar field plus a
global degree of freedom and how Horndeski theories and healthy couplings to
matter fields can be readily accommodated.
