Our youngest applied to local private schools as well. We found no difference compared to his BS application process or compare to his older brother’s application process. The local school admissions staff are salespeople, just like the BS admissions people. The results were equally surprising.
There’s not any value in trying to predict the outcomes. Substituting prediction for a solid reach/match/safety approach risks ending up empty handed (or hands full of only rejections) at the end of the process. While all of us who’ve been through the process (sometimes multiple times) have unavoidably tried to make predictions, it really only magnifies the sense of loss(es) on decision day. Better to do your best to avoid predicting and enjoy more of the sense of accomplishment from the wins on that day.