To get by with only 20 apps, you would have to be an excellent candidate. As a D.O., you will still face a few people that still have the stigma that used to be associated. For me, a top D.O. candidate=a top M.D. candidate. Not everyone shares that belief. So you need to be better than the average MD standard. Too me, that means, top quartile of class, better than average USMLE scores (average for anesth has been around 228 and 235 for steps I and II),
Also, you should know that there are many DO students out there this past year who were scoring in the 245-270 range. I think a lot of the schools teach specifically to that exam, just like the Caribbean schools do. Therefore, you see a whole bunch of really high scores. So competition is fierce just among your D.O. colleagues, because there are a bunch of candidates out there. You see some actual reports from people above who had excellent scores and only received invites from 20-30% of the programs they applied to.
If I was an "average" DO student, I would apply broadly. If you are a fourth quartile student, I would also have some contingency plans.