The authors give new characterizations for uniformly summable multiplicative functions over additive arithmetical semigroups (for the definition of uniform summable multiplicative functions over positive integers consult [the second author, Math. Z. 172, 255–271 (1980; Zbl 0416.10035); Period. Math. Hung. 17, 143–161 (1986; Zbl 0569.10024)]). The results improve those obtained in the PhD thesis of the first author [Uniformly summable multiplicative functions on additive arithmetical semigroups. Padeborn: Universität Paderborn (Diss.) (2011)] and of S. Wehmeier [Arithmetical semigroups. Paderborn: Universität Paderborn (Diss.) (2005)] and those given by W.-B. Zhang [Ramanujan J. 15, No. 1, 47–75 (2008; Zbl 1151.11051)].