You can also select a bunch of compositions in the Project Panel then press Alt/Option + \ or select File>New Composition From Selection, or right-click or drag all comps to the Create New Comp icon at the bottom of the Project panel. You will be given the option to create one comp from all selected comps or footage. If the comps have different dimensions you can choose one of them to be the master. You can also choose to overlap and create a transition between comps.
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One more important thing to remember when using this efficient technique. If you hold down the Ctrl/Cmnd key while you select you can arrange the comps in any order you like. This is what happened when I selected layer 4, 1, 2, 3 and set overlap to 15 frames and cross dissolve between layers.
I use this technique fairly often. It's a lot faster way to create a comp from multiple sources than the suggestion that imeilfx posted. I use this technique fairly often when I'm doing dynamic text animations or similar motion graphics sequences. It is important to remember After Effects is not an editing app and trying to cut sequences into a story can get incredibly cumbersome very quickly, but your workflow of creating a comp for each shot and then assembling them into a sequence is a pretty good idea more often than not.
If your comps are really complex then I would suggest rendering them to a suitable digital intermediate (DI) using a visually lossless format. These formats are often called Mezzanine Formats. The Render Cue / Output Manager is the best and fastest rendering tool for that kind of work. All of my complex projects are finalized in Premiere Pro, the audio is polished in Audition, and AE is used for effects and graphics that I cannot create directly in Premiere Pro.
I hope this helps.