This technical note considers the problem of maximizing the volume of a box of parameters that satisfy polytopic output constraints for linear fractional models using the structured singular value mu. In particular, four kinds of boxes are considered: 1) a hypercube centered at a specified location; 2) a freely located hypercube; 3) a freely located box of free shape; and 4) a freely located box of free shape and rotation. It is found that the problem for 1) can be solved by computing mu for the number of scalar constraints, while problems for 2)-4) can be reformulated as a constant-matrix mu-synthesis problem, which can be approached by D, G - K iteration.