  We consider the most general set of integrable deformations extending the
$T\bar{T}$ deformation of two-dimensional relativistic QFTs. They are CDD
deformations of the theory's factorised S-matrix related to the higher-spin
conserved charges. Using a mirror version of the generalised Gibbs ensemble, we
write down the finite-volume expectation value of the higher-spin charges, and
derive a generalised flow equation that every charge must obey under a
generalised $T\bar{T}$ deformation. This also reproduces the known flow
equations on the nose.
