We report on a systematic study of double-gap and four-gap phenolic resistive plate chambers (RPCs) for the Phase-2 upgrade of the CMS muon system at high η. In the present study, we constructed real-sized double-gap and four-gap RPCs with gap thicknesses of 1.6 and 0.8 mm, respectively, with 2-mm-thick phenolic high-pressure-laminated (HPL) plates. We examined the prototype RPCs with cosmic rays and with 100-GeV muons provided by the SPS H4 beam line at CERN. To examine the rate capability of the prototype RPCs b…