Intersections involving waves and monopoles in eleven dimensions

We consider intersections in eleven dimensions involving Kaluza-Klein monopoles and Brinkmann waves. Besides these purely gravitational configurations we also construct solutions to the equations of motion that involve additional M2- and M5-branes. The maximal number of independent objects in these intersections is nine, and such maximal configurations, when reduced to two dimensions, give rise to a 0-brane solution with dilaton coupling a=-4/9.