We study the spectral multiplicity for the direct sum A. B of operators A and B on the Banach spaces X and Y. Under some domination conditions parallel to P(B)parallel to <= C parallel to P(Lambda)parallel to(A),in particular,parallel to B-n parallel to <= parallel to Lambda(n)parallel to, n >= 0, we prove the addition formulas mu(A circle plus B) = mu(A) + mu(B) for spectral multiplicities. We give valuable new applications of the main result of the author's paper . We also use the so-called Borel transformation and generalized Duhamel product in calculating the spectral multiplicity of a direct sum of the form T circle plus A, where T is a weighted shift operator on the Wiener algebra W(D).