A drawing of a finite graph in the plane will likely result in edges crossing. The crossing number of a graph is the minimal number of edge crossings among all drawings of the graph in the plane. The crossing number is known for complete graphs having up to twelve vertices, and is conjectured to be known for thirteen vertices and above, called the Harary-Hill conjecture. A particular family of drawings which are known to satisfy the Harary-Hill conjecture are called cylindrical, or bipartite-circle, drawings of the complete graph. We describe an extension to k-partite-circle drawings of the complete graph, and study their crossing numbers.