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We apply the technique of twisted extensions of infinite-dimensional Liealgebras to find new 3D integrable {\sc pde}s related to the deformations ofLie algebra $\mathbb{R}_N[s]\otimes \mathfrak{w}$ with $N=1, 2$ as well as tothe Lie algebra $\mathfrak{h} \oplus \mathfrak{w}$, where $\mathbb{R}_N[s]$ isthe algebra of truncated polynomials of degree $N$, $\mathfrak{w}$ is the Liealgebra of polynomial vector fields on $\mathbb{R}$ and $\mathfrak{h}$ is theLie algebra of polynomial Hamiltonian vector fields on $\mathbb{R}^2$.

Lax representations via twisted extensions of infinite-dimensional Lie algebras: some new results