Unlikely intersections in products of families of elliptic curves and the multiplicative group

Let Eλbe the Legendre elliptic curve of equation Y2= X (X - 1)(X - l). We recently proved that, given n linearly independent points P1(l), ¼, Pn(l) on Eλwith coordinates in (l), there are at most finitely many complex numbers l0such that the points P1(l0), ¼, Pn(l0) satisfy two independent relations on El0. In this article, we continue our investigations on Unlikely Intersections in families of abelian varieties, and consider the case of a curve in a product of two non-isogenous families of elliptic curves and in a family of split semi-abelian varieties.