Can Damon Braces fix an overbite, 4mm overjet and crowding WITHOUT tooth extractions?

I got traditional braces two weeks ago and I need to get 4 tooth extractions pretty soon. The first premolars on the top and the second premolars on the bottom. I did the research AFTER I got the braces on, which was my mistake but I found that tooth extractions cause a TON of issues. Including a "flat profile"? I'm wondering if switching over to Damon Braces would be an option for me to fix my teeth without removing any healthy ones.