In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum${\left(k\right)}_F$ of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum${\left(k\right)}_F$ is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...