This paper is the continuation of the author's paper entitled the same name. We first introduce the notion of multiply commutative ideals in BCK-algebras, and investigate a number of their properties similar to $n$-fold commutative ideals. And then we clarify the essential attribute and some other properties of normal ideals (which were called $n$-fold weak commutative ideals) in BCK-algebras. Finally, we discuss various relations among multiply implicative ideals, multiply commutative ideals and normal ideals.