Asking for more financial aid

Is it possible? Any advice?

If you have a better package from a comparable college (same or higher ranking) you can ask for a review of your FA package and let them know that you have a package with a lower cost of attendance at school X. It may or may not help. Also, if you have additional info that you think they may not have taken into account (recent job loss, illness with high medical bills, etc) you can ask them to consider that.