You can do additive and additive-like synthesis with ZynAddSubFX, but instead of using per-harmonic envelopes and shift amounts, you can control the bandwidth and spacing of each harmonic.

To mimic an existing sound, such as an organ, I once used audio software to plot the FFT of the original sound, then manually entered the amplitudes of the fundamental and harmonics in a ZynAddSubFX XML instrument definition. I'd like something that automates that process.

Edit: regarding spectral manipulation, there is also SpectraLayers.