  In this study, we investigate various deformations within the framework of
Bondi-van der Burg-Metzner-Sachs invariant field theory (BMSFT). Specifically,
we explore the impact of Bondi-van der Burg-Metzner-Sachs (BMS) symmetry on the
theory by introducing key deformations, namely, $T \overline{T}$, $JT_{\mu}$,
and $\sqrt{T \overline{T}}$ deformations. In the context of generic seed
theories possessing BMS symmetry, we derive the first-order correction of
correlation functions using the systematic application of BMS symmetry ward
identities. However, it is worth noting that higher-order corrections are
intricately dependent on the specific characteristics of the seed theories. To
illustrate our findings, we select the BMS free scalar and free fermion as
representative seed theories. We then proceed to analytically determine the
deformed action by solving the nontrivial flow equations. Additionally, we
extend our analysis to include second-order deformations within these deformed
theories.
