  We establish a quantisation of corner-degenerate symbols, here called
Mellin-edge quantisation, on a manifold $M$ with second order singularities.
The typical ingredients come from the "most singular" stratum of $M$ which is a
second order edge where the infinite transversal cone has a base $B$ that is
itself a manifold with smooth edge. The resulting operator-valued amplitude
functions on the second order edge are formulated purely in terms of Mellin
symbols taking values in the edge algebra over $B.$ In this respect our result
is formally analogous to a quantisation rule of a joint paper with J. Gil and
J. Seiler for the simpler case of edge-degenerate symbols that corresponds to
the singularity order 1. However, from the singularity order 2 on there appear
new substantial difficulties for the first time, partly caused by the edge
singularities of the cone over $B$ that tend to infinity.
