We propose high-radix microfluidic multiplexers that effectively address a large number of flow channels with a few control lines having pressure valves of different thresholds. Previous binary multiplexers address only two flow channels by controlling identical threshold pressure valves in two control lines; that is, they address 2(n/2) flow channels by using n control lines. However, the proposed ternary or quaternary multiplexer (high-radix multiplexers) addresses three or four flow channels by controlling two or three kinds of pressure valves in two control lines, respectively. Thus, these multiplexers address 3(n/2) and 4(n/2) flow channels, which are results of increasing the radix from binary to quaternary. In experiments, we designed ternary (two kinds of valves) and quaternary (three kinds of valves) multiplexers and applied them to 3 x 3 and 4 x 4 well arrays with four control lines, respectively. We determine the static/dynamic operating conditions of the pressure valves having different thresholds in the ternary and quaternary multiplexers. Under these conditions, the ternary and quaternary multiplexers successfully address 3 x 3 and 4 x 4 well arrays by controlling two and three pressure valves of different thresholds in four control lines, respectively.