An electron cooling system and method for increasing the phase space intensity and overall intensity of ion beams in multiple overlap regions, including a vacuum chamber to allow a single electron beam to be merged and separated with multiple ion beams, an electron supply device including a cathode to generate the electron beam, an electron collector device including a collection plate to collect the electron beam, multiple magnetic field generation devices to guide the electrons on their desired trajectories, and multiple electrodes to set the velocity of the electron beam independently in each overlap region. By overlapping the electron and ion beams, thermal energy is transferred from the ion beams to the electron beam, which allows an increase in the phase space density and overall density of the ion beams. Advantageously, the electron cooling system uses multiple magnetic field generation devices to guide the electrons into and out of multiple, separate, ion beam overlap regions, allowing the single electron beam to cool an ion beam in more than one overlap region. Advantageously, the electron cooling system uses electrodes to control the mean electron beam velocity in each overlap region, allowing for mitigation of electron beam emittance growth caused by scattering that occurs exterior to the overlap regions. Advantageously, the electrodes used to control the mean electron beam velocity in each overlap region allow for a single electron beam to achieve different velocities to match different desired ion beam velocities in the multiple overlap regions.