  In this note we explore the notion of everywhere almost summing polynomials
and define a natural norm which makes this class a Banach multi-ideal which is
a holomorphy type (in the sense of L.Nachbin) and also coherent and compatible
(in the sense of D. Carando, V. Dimant and S. Muro) with the notion of almost
summing linear operators. Similar results are not valid for the original
concept of almost summing polynomials, due to G. Botelho.
