  In this paper we consider a multiparametric version of Wolfgang Schmidt and
Leonard Summerer's parametric geometry of numbers. We apply this approach in
two settings: the first one concerns weighted Diophantine approximation, the
second one concerns Diophantine exponents of lattices. In both settings we use
multiparametric approach to define intermediate exponents. Then we split the
weighted version of Dyson's transference theorem and an analogue of
Khintchine's transference theorem for Diophantine exponents of lattices into
chains of inequalities between the intermediate exponents we define basing on
the intuition provided by the parametric approach.
