This work examines the stability of gray in transmissive films as a function of variations in the dye amounts of cyan, magenta, and yellow. The variation was confined to 10% of the combined, total dye amount. The volume defined by these variations mapped into XYZ-color space was used as a metric. The dye density functions were modeled with normal distributions. Their widths and peak positions were parameterized for optimization. For each width a dye set of maximum stability was found. At widths below 50 nm, the narrower the spectral density functions, the higher the stability. However, narrower sets have the drawback of requiring larger dye amounts. At widths below 25 nm the dye amounts or equivalent optical densities become unrealistic high (larger than 3). The color stability comes at a high price: the sets with maximum stability have a severely reduced color gamut; though, substantially larger gamuts can be obtained, i.e., multiple times larger, if the restriction of high stability is a little bit relaxed.