We consider weighted block designs and complete Steiner systems, and compare them with totally symmetric $(n,m)$-quasigroups. We show that a complete Steiner system $S'(2,k,v)$ is equivalent to a totally symmetric $(2,k-2)$-quasigroup, and that any complete Steiner quadruple system $S'(3,4,v)$ is equivalent to a totally symmetric $(3,1)$-quasigroup.