We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from pair conserved $U(1)$ currents $J^a$. propose formulation these deformations, based on the gauging corresponding symmetries in path integral. This formalism leads to an exact dressing $S$-matrix system, similarly as what happens case $\mathrm{T}\overline{\mathrm{T}}$ deformati...