  A multiparameter filtration, or a multifiltration, may in many cases be seen
as the collection of sublevel sets of a vector function, which we call a
multifiltering function. The main objective of this paper is to obtain a better
understanding of such functions through multiparameter discrete Morse (MDM)
theory, which is an extension of Morse-Forman theory to vector-valued
functions. Notably, we prove algorithmically that any multifiltering function
defined on a simplicial complex can always be approximated by a compatible MDM
function. Moreover, we define the Pareto set of a discrete multifiltering
function and show that the concept links directly to that of critical simplices
of a MDM function. Finally, we experiment with these notions using triangular
meshes.
