Grothendieck–Pietsch composition results for multiple summing operators

We prove Grothendieck–Pietsch composition results for multiple summing operators without a linear analogue. As application, we give a new proof for the multilinear version of Grothendieck’s composition theorem proven by D. P érez-García and I. Villanueva. We use this result in tandem with the Maurey factorization theorem, to find the necessary and sufficient conditions for multilinear multiplication operator from a product of $$l_{p}$$ spaces into $$l_{1}$$ to be multiple 2-summing.