We obtain a classical spin liquid (CSL) phase by applying a magnetic field to the J 1 -J 2 -J 3 Ising model on a kagome lattice. As we proved in the previous study [Phys. Rev. Lett. 119, 077207 (2017)], this model realizes one species of CSL, the hexamer CSL, at the zero magnetic field, which consists of macroscopically degenerate spin configurations with mixed total magnetization, M. The magnetic field selects its subset, which can be mapped to a trimer covering of the dual lattice and forms a magnetization plateau of M = 1/9. In addition to this CSL, we find two other magnetization plateaus at M = 5/9 and 17/27, which are ascribed to the "multimer" superstructures on a dual lattice.