  In this paper, we explore the concept of multilinear operators that are
multiple almost summing and present a new concept of type and cotype of
multilinear operators and investigate the conditions for this new concept to
recover the original concept of type and type for multilinear operators. We
also show that these classes are Banach multi-ideals and establish the
coherence and compatibility of these classes with the generated homogeneous
polynomials.
