  We introduce a notion of $(p,q)$-dominated multilinear operators which stems
from the geometrical approach provided by $\Sigma$-operators. We prove that
$(p,q)$-dominated multilinear operators can be characterized in terms of their
behavior on finite sequences and in terms of their relation with a Laprest\'e
tensor norm. We also prove that they verify a generalization of the Pietsch's
Domination Theorem and Kwapie\'n's Factorization Theorem. Also, we study the
collection $\mathcal{D}_{p,q}$ of all $(p,q)$-dominated multilinear operators
showing that $\mathcal{D}_{p,q}$ has a maximal ideal demeanor and that the
Laprest\'e norm has a finitely generated behavior.
