This may not exist as a product or tool, but it should.
37 track multi-track show. Many tracks one above the other. Select all the tracks. Effect > Amplify > -1.
Amplify adjusts all the selected tracks so the Stereo Mixdown comes out without overloading or clipping. I picked Amplify because Normalize would be a nightmare.
I think I prefer the idea of a “Master Fader” on the Mixer Board that moves all selected faders (and so all track gain sliders) in unison. This way would be non-destructive.
No reason that I can think of for not having both options.
Audacity would need to calculate the peak amplitude of the mix (Audacity “knows” the peak amplitude of each track, but it does not know what the peak of the sum of multiple tracks will be without calculating the sum for each sample period), then from that work out the necessary amplification.
I prefer the idea of making the computer do the scut work. Both tools are valuable, but the Master Fader demands recursive efforts to find the sweet spot.
Three very good reasons to use 32-bit float for multi-track projects:
Safeguard against clipping when mixing.
No dither noise when processing tracks.
With a lot of simultaneous tracks, the tracks will probably need to be at a very low level (to avoid clipping the mix). 32-bit float preserves the dynamic range and SNR.