A Bohr classical model for He is applied to multiply charged ions colliding with He at intermediate energies. Reactions studied are single-electron capture, single and double ionization, and electron-capture ionization for projectile charge states q = 1+ to 100+, and the energy range E = 1--5 MeV/amu. The dominant electron-removal collision process is single ionization. For the higher-charge-state ions, single-charge exchange is found to be primarily due to transfer ionization, a two-electron process where one electron is ionized and the other is captured by the projectile. For low-charge states, the single- and double-ionization cross sections are close to the expected q/sup 2/ and q/sup 4/ scaling. The calculations are in reasonable agreement with available experimental data.