First off, sorry I haven't been able to post in a while-- I've been working very hard on my college applications lately.
Many private colleges are member colleges/universities of the Common Application-- Common App for short. It's a handy website that allows you to have one app and send it to many of these schools. For each school, the only thing you have to do differently is fill out each respective school's "Supplement," which varies from school to school.
Some schools you may be familiar with on the Common App include USC, Stanford, Yale, Harvard, Northwestern, and many other schools.
https://www.commonapp.org/CommonApp/default.aspx