This paper gives results for the spectrum, all allowed E1 radiative partial widths (and some important M1 widths) and all open-charm strong decay amplitudes of all 40 cc̄ states expected up to the mass of the 4S multiplet, just above 4.4 GeV. The spectrum and radiative widths are evaluated using two models, the relativized Godfrey-Isgur model and a nonrelativistic potential model. The electromagnetic transitions are evaluated using Coulomb plus linear plus smeared hyperfine wave functions, both in a nonrelativistic potential model and in the Godfrey-Isgur model. The open-flavor strong decay amplitudes are determined assuming harmonic oscillator wave functions and the P30 decay model. This work is intended to motivate future experimental studies of higher-mass charmonia, and may be useful for the analysis of high-statistics data sets to be accumulated by the BES, CLEO, and GSI facilities.