  It has been recently discovered that the $\text{T}\bar{\text{T}}$ deformation
is closely-related to Jackiw-Teitelboim gravity. At classical level, the
introduction of this perturbation induces an interaction between the
stress-energy tensor and space-time and the deformed EoMs can be mapped,
through a field-dependent change of coordinates, onto the corresponding
undeformed ones. The effect of this perturbation on the quantum spectrum is
non-perturbatively described by an inhomogeneous Burgers equation. In this
paper, we point out that there exist infinite families of models where the
geometry couples instead to generic combinations of local conserved currents
labelled by the Lorentz spin. In spirit, these generalisations are similar to
the $\text{J}\bar{\text{T}}$ model as the resulting theories and the
corresponding scattering phase factors are not Lorentz invariant. The link with
the $\text{J}\bar{\text{T}}$ model is discussed in detail. While the classical
setup described here is very general, we shall use the sine-Gordon model and
its CFT limit as explanatory quantum examples. Most of the final equations and
considerations are, however, of broader validity or easily generalisable to
more complicated systems.
