Secant defectivity of projective varieties is classically approached via dimensions of linear systems with multiple base points in general position. The latter can be studied via degenerations. We exploit a technique that allows some of the base points to collapse together. We deduce a general result which we apply to prove a conjecture by Abo and Brambilla: for c≥3 and d≥3, the Segre-Veronese embedding of Pm×Pn in bidegree (c,d) is non-defective.