  A proposal for constructing a universal nonlinear ${\hat W}_{\infty}$ algebra
is made as the symmetry algebra of a rotational Killing-symmetry reduction of
the nonlinear perturbations of Moyal-Integrable deformations of $D=4$ Self Dual
Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket
based on nonlinear gauge theories associated with infinite dimensional Lie
algebras. A Quantization and supersymmetrization program can also be carried
out. The relevance to the Kadomtsev-Petviashvili hierarchy, $2D$ dilaton
gravity, quantum gravity and black hole physics is discussed in the concluding
remarks.
