The early phase of design contains multiple sources of unexpected circumstances which include the change or addition of performance requirements or design conditions with the process of the design phases. Therefore, designers are required to design considering those unexpected circumstances in the after phases. Previously, we proposed a preference set-based design (PSD) method, which obtains a unique design solution set from a point of view of design preference and robustness under various sources of uncertainties while incorporating the designer's preference in the early phase of design. PSD method represents the uncertain design information as the interval set. This paper proposes a new design method based on PSD method which can obtain diverse possible design solution sets for unexpected circumstances by deriving the multiple feasible design domains which satisfy the required performances. Obtaining diverse possible design solution sets could deal with the unexpected circumstances by selecting the optimal design solution from obtained diverse possible design solution sets in the early phase. In this paper, the proposed design method is applied to the design problem of an active isolation system of 4-story building to correspond to the additional unexpected earthquake ground motion which the designer cannot consider at the early phase of design.