The merit aid landscape has 2 components. One, the guaranteed merit aid based on stats. Two, variable, discretionary aid schools use to entice students who most likely wouldn’t otherwise attend to enroll in their universities.
Once you understand that that’s what’s driving the merit bus for schools in the 2nd category, you can make a list of schools offering merit aid, and from that list, figure out if your student has something the school really wants.
Usually that’s better grades/scores than their usual accepted candidate, but sometimes there are other institutional needs that can be known (and some that can’t). An example of institutional needs other than academics would be schools that are looking to boost their diversity, or geographical reach (for a regional school hoping for a more national reputation).
But most merit is offered for academics. A basic rule of thumb is that your student will get no merit at their reach schools, some aid at target schools, maybe, and the most aid at their safeties. So – clearly you need to be focusing most of your attention on the safeties. I believe the most aid from private schools is $30,000/year (barring some named scholarship that you usually have to apply for)).