Neural-Matrix style, high-density electrode arrays for brain-machine interfaces (BMIs) and neuroscientific research require the use of multiplexing: Each recording channel can be routed to one of several electrode sites on the array. This capability allows the user to flexibly distribute recording channels to the locations where the most desirable neural signals can be resolved. For example, in the Neuropixel probe, 960 electrodes can be addressed by 384 recording channels. However, currently no adaptive methods exist to use recorded neural data to optimize/customize the electrode selections per recording context. Here, we present an algorithm called classification-based selection (CBS) that optimizes the joint electrode selections for all recording channels so as to maximize isolation quality of detected neurons. We show, in experiments using Neuropixels in non-human primates, that this algorithm yields a similar number of isolated neurons as would be obtained if all electrodes were recorded simultaneously. Neuron counts were 41-85% improved over previously published electrode selection strategies. The neurons isolated from electrodes selected by CBS were a 73% match, by spike timing, to the complete set of recordable neurons around the probe. The electrodes selected by CBS exhibited higher average per-recording-channel signal-to-noise ratio. CBS, and selection optimization in general, could play an important role in development of neurotechnologies for BMI, as signal bandwidth becomes an increasingly limiting factor. Code and experimental data have been made available.