Add harmonics to a FFT decomposed signal
For each added harmonic, for each bin number below N/2, you could divide by the harmonic ratio, then use that resulting number to interpolate a point below in the FFT, unless the division results in an integer, in which case you could just use the value from a lower FFT bin.  Use a high-quality interpolator, such as a windowed Sinc or other polyphase upsampling filter kernel.  For a strictly real result from an IFFT, make sure the values above N/2 in your harmonic frequency synthesis remain conjugate symmetric with those below N/2.