Adjusting signal-to-noise ratio for a speech in noise experi

Is there a way to automatically adjust the SNR by entering the desired outcome somewhere?

This may be harder than you think. Most of the volume control tools in Audacity work on peak values. For example, if you Effect > Amplify and leave the settings alone, it will change the waveform peak values to 0dB. Loudness, RMS or any other value is undefined.

If I had to put two different tracks in one show, I’d just import two different tracks. Audacity will install them one above the other and try to play them at the same time. From there, you can select one track or the other for modification. If you do nothing else but export a sound file, Audacity will mix them together into one show.
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I know you can measure this backwards. Perform some change on the timeline and use Analyze > Contrast: Measure Selection (write it down) > Close. That will tell you the RMS/Loudness value of the work.

You might also use RMS Normalize. That’s from the Audiobook tools. The audiobook people require submissions to conform to strict technical guidelines.