Just so you're clear
@St***
right now people who enroll in private schools (“โรงเรียนนอกระบบ”) cannot get Non-ED visas from thai consulates in other countries and request permission to enter thailand. :/
AND
as people pointed out IF you got a Special Tourist Visa while you could indeed stay here almost 9 months you could not change that visa to another type inside the country at the immigration office.
IF you're not intending to enroll in a real university for a real degree (which you could get the ED visa from the consulate in your country and then request permission to get in) your best bet is to get a single entry tourist visa, come here get stamped in for 60 days and then make the rounds to some potential schools you are interested in.