In this paper, a new space compactor, called an augmented multimode compactor, is presented. Accordingly, scan chains are separated into groups using t orthogonal partitions. The augmented multimode compactor has three modes such that all scan chains, a group of scan chains and an intersection of two groups of scan chains is selected for compression. Respectively, 1, kt-1 and any number of unknown states per shift-out cycle can be tolerated in these modes where k is the number of the compactor outputs assigned for observation of each scan chain. Simulation results demonstrate the efficiency of the proposed principles for constructing fully X-tolerant compactors. In the range of 0 to 10 percent of unknown states in test responses, the proposed scheme achieved the same or up to 3 times better observability than the fully X-tolerant combinational compactor.