The paper is concerned with a simplicial composition of two different positive approximation processes on a finite real interval in order to construct a positive approximation process on a simplex. The general method is illustrated by considering the sequences of Bernstein and Stancu operators. Estimates of the rate of convergence and a Voronovskaja type formula for the resulting operators are obtained. The construction is motivated by applications to the approximation of the solutions of suitable evolution problems, e.g., problems connected with the Fleming-Viot models in population genetics.