  In a recent series of papers by Lou et al., it was conjectured that higher
dimensional integrable equations may be constructed by utilizing some
conservation laws of (1 + 1)-dimensional systems. We prove that the deformation
algorithm introduced in arXiv:2211.06844, applied to Lax integrable
$(1+1)$-dimensional systems, produces Lax integrable higher imensional systems.
The same property is enjoyed by the generalized deformation algorithm
introduced in [Lou,Jia,Hao. Chinese Phys. Lett. 2023]; we present a novel
example of a $(2+1)$-dimensional deformation of KdV equation obtained by
generalized deformation. The deformed systems obtained by such procedure,
however, pose a serious challenge because most of the mathematical structures
that the $(1+1)$-dimensional systems possess is lost.
