Optimal colours for human vision occur on the boundary of a three-dimensional object-colour solid, and result from optimal reflectance spectra that take on only the values 0 and 1, with at most two transitions between those values. Different illuminants lead to different solids. If there are two illuminants and a single sensing device, then we can construct a six-dimensional double object-colour solid by concatenating colour signals from both illuminants. Colours on the boundary of a double-object solid, and the spectra that generate them, can also be called optimal. This article shows that, while optimal spectra for double solids take on only the values 0 and 1, there is no maximum number of transitions between those values: given a device, we can always construct two illuminants such that the resulting double object-colour solid has an optimal reflection spectrum with as many transitions as desired.