This could be common knowledge and I'm just late to the party, or there is possibly a better way to do this. Note that I've been producing for a long time, but I only made the full switch to Live about a year ago.
All that being said ...
I have been using Live to produce some tech/bass house and nu-disco tracks for a vocal artist and her label. They want both club mixes and shorter "radio friendly" versions of these songs in parallel.
So, I've been doing the longer club mixes with additional parts and longer sections as my master Live project, then creating one or more dedicated editing sub-projects to slice and dice the stereo master track down to radio and/or social media friendly versions.
For these songs, I'm finding that the differences in overall sound for the target mixes can be managed in the Main audio channel if that's a requirement for the particular song.
So, once I have a track/song project reasonably complete and ready for the club, the sub-project steps are as follows:
1) Export audio from the master "club track" project using a consistent name, such as "songname_to_remix.wav". Once exported, I do NOT number or otherwise change the name of this export for any subsequent updates. This export is different than exports that I intend for submission/sharing/listening. It is internal to my work and meant to feed the radio edit sub-project.
1.a) If a change in the Main audio chain is needed for the radio edit, when exporting I disable effects on the master club mix Main audio channel to get an unprocessed mix out. I always reenable the Main effects once export is done.
2) I create a new blank Live subproject named accordingly, such as "songname_radio".
2.a) IF I am exporting an unprocessed mix without the Main channel effects, I will need to create new Main channel effects in this radio subproject OR I just copy the effects chain from my club mix project's Main channel to have a baseline starting point for my radio mix version of the Main channel and effects. Any Main channel and effects automation, I copy over as well.
3) I import my "songname_to_remix.wav" file to a stereo audio track in the new project.
4) Now I am free to slice, dice, edit and enhance that audio track until I have the shorter radio version, ready for export and submission/sharing/listening.
4.a) I can also add any additional musical elements unique to the radio mix on new tracks in the project.
5) I optionally repeat steps 2-4 for any OTHER remixes needed, such as "songname_socialmedia".
Here's the fun thing: outside of any possible Main channel differences, almost any changes made to my master club mix Live project (and reexported) will AUTOMATICALLY be reflected in the radio mix sub project because the source material is automatically updated.
If needed, I can always expand this method to use stems instead of a stereo mix for finer control.
I haven't done this yet, but the entire process should work in the other direction, where one could create the shorter "radio friendly" song as the master project with the club mix being the sub-project, where you EXPAND the original version of the song. Just depends on your personal needs.
Anyway, this has been working well for me and gives me a fast turnaround time for work-in-progress updates, where any significant changes or improvements to the master project are almost automatically shared across the different sub-project versions. Note that if you change arrangements of the master song project or otherwise make changes that "break" your sub-project and its transitions, you'll need to revisit and edit the sub-projects too. But if your master project arrangement is stable, this works REALLY well, at least for me.
There might be some Live pros here that are already either doing something like this or have even better methods in their toolbelt. Even so, it this helps even one person to better manage multiple song versions, it's a win for me.
Cheers!