Every single year, kids with SSAT scores above the 95th percentile are rejected from top schools in favor of kids with lower scores who have more compelling essays, stronger teacher recommendations, ECs that align better with the school’s offerings, or come across as kinder/nicer. Every. Single. Year.
A score in the 85th percentile tells the school you can handle the academics.
Having an even higher score does not necessarily help. It is unlikely to be tie breaker like better teacher recommendations, essays, and ECs, all of which carry more weight provided your SSAT score indicates you can handle the pace of the academics.
Those 2-3 hours a day people are suggesting you spend studying to raise your score? They are better spent improving your cross country times, increasing your ranking in tennis, or submitting your best writing for publication or awards.