This paper considers the problem of characterizing the sets of consistent and inconsistent parameters for given constraints for linear fractional models. Based on previous results on the single box volume maximization problem using structured singular value, algorithms that express the (in)consistent parameter set as a union of multiple boxes are developed. Since no relaxation is involved in the proposed algorithms, the obtained sets are guaranteed to be (in)consistent with the given constraints even when the real set of (in)consistent parameters is nonconvex. A numerical example is included to illustrate the difference of the sets obtained by the proposed algorithms.