  The Klein-Gordon equation, one of the most fundamental equations in field
theory, is known to be not invariant under conformal transformation. However,
its massless limit exhibits symmetry under Bekenstein's disformal
transformation, subject to some conditions on the disformal part of the metric
variation. In this study, we explore the symmetry of the Klein-Gordon equation
under the general disformal transformation encompassing that of Bekenstein and
a hierarchy of `sub-generalisations' explored in the literature (within the
context of inflationary cosmology and scalar-tensor theories). We find that the
symmetry in the massless limit can be extended under this generalisation
provided that the disformal factors takes a special form in relation to the
conformal factor. Upon settling the effective extension of symmetry, we
investigate the invertibility of the general disformal transformation to avoid
propagating non-physical degrees of freedom upon changing the metric. We derive
the inverse transformation and the accompanying restrictions that make this
inverse possible.
