Different ion channel combinations can yield equivalent neuronal excitability. This degeneracy facilitates robust regulation of excitability by enabling a disruptive change in one channel to be offset by compensatory changes in other channels. But various aspects of excitability plus other cellular properties require regulation. Coordinately regulating multiple properties via control of overlapping sets of ion channels is no easy task. Here we demonstrate that of the many ion channel combinations producing the target value for one property (the single-output solution set), few combinations produce the target value for other properties. Combinations producing the target value for two or more properties (the multi-output solution set) correspond to the intersection between single-output solution sets. We demonstrate that for multi-output solution sets to be degenerate, the number of controllable ion channels (nin) must exceed the number of regulated properties (nout). We further demonstrate how the dimensionality of solution space shapes ion channel correlations that emerge during homeostatic regulation and how homeostatic regulation may fail given the heightened challenge of simultaneously regulating many properties.SIGNIFICANCE STATEMENTNeurons, like other cells, must continue functioning despite variations in their operating conditions. In particular, they must adjust their intrinsic excitability to maintain their information processing capabilities. Neurons homeostatically regulate their excitability and other properties by up- or down-regulating, or otherwise modulating, myriad different ion channels. But each ion channel tends to affect several properties; consequently, adjusting an ion channel to regulate one property is liable to disrupt another property. Instead, multiple ion channels must be adjusted. Specifically, we show that in order to regulate n properties, n+1 ion channels must be adjustable. This has a simple mathematical explanation but important biological implications. The need to simultaneously regulate many properties may help account for ion channel diversity.