Yes. If yes, please describe your company’s procedure:

I work as a freelancer, so my procedure is my own. Even when I was a wage slave, I didn't use any levels of edit approach because I believe (and teach, when I teach editing) that as an editor, it's my responsibility to do whatever is required to produce a manuscript the author can be proud of and that the audience will understand. When time is constrained, I use triage as the basis for my levels of edit: I focus on the crucial problems (the ones that will kill understanding) before working on the merely important ones (the ones that will only impede understanding), and lastly I remove the blemishes (things worth fixing but that won't impede or kill understanding) if time permits. Most "levels of edit" systems I'm familiar with don't understand the importance of triage.