You should use a dedicated MP3 editor—assuming the work is simple cutting and arranging.
MP3 editors know how to work on the MP3 data without applying recompression.
If you need anything more complicated than that, say effects or filters, then you’re stuck with Audacity. At the end of the edit session your choices are File > Export the show at the same sound quality but much larger file size (by choosing a much higher MP3 Quality), or Export the same filesize at lower sound quality. Nobody wins.
A show backup and archive should be a WAV (Microsoft) 16-bit sound file, not an Audacity Project.
A note: The first option, Exporting the show at a higher MP3 quality doesn’t guarantee a perfect sounding show. All that does is reduce the sound damage increase. The only way to make the damage increase be zero is Export as a WAV or other uncompressed file format, which I assume you don’t want to do.
MP3 is a final step or product, not part of an edit session.
Yes, I know ACX AudioBook requires submission in MP3, but they also require really, really high MP3 compression quality (Mono presentation at 192 quality or higher) and our recommendation is save your own personal archive as WAV.