From reading through this thread, I believe you may request for priority processing under extenuating circumstances. Before submitting your application, cases with family violence or abuse can be indicated on the application envelope (paper application only. For online applications, maybe a webform). And they will give it priority and process in a couple of months.
If you already have AIP and awaiting final decision, you can request for priority processing where for example you have a pending school start date (you email your BRO with the admission letter and explain that you need your COPR or may lose your spot) and they will process your second stage approval much faster. I read a case on here where the poster was in this exact situation.
I can't think of any situation that would make them process a stage one application with priority though. I hope this helps.