Summary: In the paper [Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 49, 179–185 (2019; Zbl 1438.20079)] we dealt with some basic functional equations on an infinite hypergroup join. The special property of that join is that every non-identity element is of infinite order, i.e. no power of it is the identity, but there is no nonzero additive function on this hypergroup. In this paper we extend the ideas to construct an infinite join starting from arbitrary finite hypergroups and we describe some basic function classes on this hypergroup.