  In this paper we provide an abstract aproach to the study of classes of
multiple summing multilinear operators between Banach spaces. The main purpose
is unify the study of several known classes and results, for example multiple
$(p, q_1,\dots, q_n)$-summing operators, multiple mixing $(s, q, p)$-summing
operators and multiple strong $(s, q, p)$-mixing summing operators. We also
define new class of multiple summing multilinear operator that are particular
cases of our construction and, therefore, satisfy the results proved in the
paper.
