  We explore whether one can $T \overline{T}$ deform a collection of theories
that are already $T \overline{T}$-deformed. This allows us to define classes of
irrelevant deformations that know about subsystems. In some basic cases, we
explore the spectrum that results from this procedure and we provide numerical
evidence in favor of modular invariance. We also study the flow of the
classical Lagrangian for free bosons and free fermions under successive
deformations. Some of the models found by sequentially flowing are likely to
have interesting holographic interpretations.
