Only detect the phase of a sinusoid multiplexed with other sinusoids of different frequencies
This seems like an irrelevant hypothetical problem but I have done the reverse to show what you might have to do.
If you had a 5 stage binary counter with f=320 Hz then subharmonics from f/2 to f/32 with coherent phase (0deg) for each sine and equal amplitude (-20dB) all mixed together. It would look like below in red. The yellow trace shows only the analog component of the lowest frequency by pointing at it.
I did this with Falstad's Fourier Spectrum analyzer/synthesizer and manually adjusted the spectrum per your question for each binary sub-harmonic signal with ~0deg phase difference.
The result was starting to look like a messy recursive sin(x)/x modulated carrier with a peak that was 16dB above the amplitude of each frequency at the frequency of f/32=10Hz.

Now to get this spectral density result for amplitude and phase you must do the reverse of what I did.
But what's the point?
Added
Ok you want some log2(f) signal phase detectors. But why not use a sinx/x pulse to cover say 2 decades then compare the input and output to get the transfer function with all the linear harmonics instead of only binary sub-harmonics.