The authors fabricated highly doped Si single-electron transistors (SETs) with three islands. The valley current of the obtained Coulomb oscillation was systematically investigated in comparison with the cotunneling theory. The temperature dependence of the valley current was well described by the inelastic cotunneling theory above 40 K in the low drain voltage region. Since the inelastic cotunneling current was confirmed to be dominant in the high temperature region and is exponentially suppressed by multiplexing islands, SETs with multiple islands are promising for the practical application such as reliable circuit operations.