We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction V down arrow X is multiplicity-free. In this paper we handle the case where X is of type A, and is irreducibly embedded in Y of type B, C or D. It turns out that there are relatively few triples for X of arbitrary rank, but a number of interesting exceptional examples arise for small ranks. (c) 2021 Elsevier Inc. All rights reserved.