In earlier work [P.J. Aston, R. Shail, The dynamics of a bouncing superball with spin, Dyn. Sys. 22 (2007) 291–322] the problem of the possible back and forth motion of a superball thrown spinning onto a horizontal plane was considered in detail. In this paper the problem is extended to include a vertical wall. In particular motion of the superball where it bounces alternately on the floor and the wall several times is considered