Two new excited states, S2c(3185)0 and S2c(3327)0, are observed in the E thorn c K- invariant-mass spectrum using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb-1. Five previously observed excited S20c states are confirmed, namely S2c(3000)0, S2c(3050)0, S2c(3065)0, S2c(3090)0, and S2c(3119)0. The masses and widths of these seven states are measured with the highest precision to date.