If superimposed dimension count as such higher dimensions and there can be three orthogonal axes in 3D space the last providing chirality.
There are two other dimensions in space and then three in time, for a total of five possible dimensions to superimpose on. Including the mandate (un-imposed), that we exist in, five superimpose dimensions and six existing dimensions for a total of thirteen dimensions.
One higher dimension is three space plus time superimposed on another one dimension.
Superposition will explain how particles are made to radiate photons.
They started as a superposition of a photon and a particle in the first place. Orthogonality restricts the types of superposition possible and so limits the types of photons emitted or not at all.