Eliashberg's h-principle for maps with Thom-Boardman singularities

Suppose we are given smooth manifolds $M$, $N$ and a continuous map $f:M\to N$. We may ask, when is $f$ homotopic to a smooth map with a prescribed singular locus? The case of fold singularities was settled by Y.Eliashberg in the 1970s. Namely, there is a necessary and sufficient condition for $f$ to be homotopic to a smooth map with prescribed folds $C\subset M$ and with no other critical points. We will discuss how one can generalize this condition for an arbitrary locus of Thom-Boardman singularities.