thanks for your question, Kyle, comping is no doubt a key part of the recording workflow. some daws have this as a slightly more intuitive automatic feature, & it would be nice to see something similar in live. with a combination of keyboard shortcuts & the particulars of arrangement mode, however, the manual method for accomplishing this can be almost as speedy & actually give you more options. let's look through how we might do this -
you don't have to start with looped recording but it's a pretty standard way to quickly get multiple takes without breaking the flow. you can take several stabs at small passages (as I am here) or work on whole sections or even whole songs.
it can feel like a pain to copy/paste this around & get all the takes in order but it can go really quick if you make use of a few shortcuts. start with cmd + t to create a blank track, hold option & drag the recording into it to create a copy.
take a look at the sample display in the copied clip & you'll see the loop bracket, engaged or not, defines the exact length of the take, not the full recording. we'll use this to our advantage - drag the end of the loop bracket back to the start marker of the current clip. now the loop bracket will perfectly surround the previous take & by turning "loop" on & off the active portion of the recording will snap to the previous take. repeat this process for as many takes as you recorded in your loop.
once these are all laid out you'll want to audition the different takes & identify the successful portions of each. select the parts you like & don't worry about getting too exact - you can adjust the clip size later during assembly. use the shortcut cmd + e to split the clips out. it can be useful to change the color of the extraction to differentiate it & you can even rename the clip with an identifier of some sort if necessary.
with all the best parts identified, you can easily delete all the superfluous material. from here, you can see which take had the biggest chunk of "good" & use that as the comp track. just drag in the other clips to fill in the gaps.
take some time to go over where the clips meet each other & ensure there is no ugly overlap - especially if you're comping vocals. you can easily clean this up by dragging one clip over the other. it will likely be handy to use fades at some point so you can transparently fade between clips & using the shortcut cmd + option + f can pull these up for you.
finally, delete the muted alternate take tracks. select your patchwork of "best clips" & consolidate them using cmd + j.
& there you have it, a complete & compiled clip & no-one need ever know it was stitched together from a number of takes. thanks for your question, Kyle, I hope that gives you some ideas!
if you have a question about some ableton workflow or another, ask me on twitter!