There are annual federal student loan borrowing limits. Currently a college undergraduate can borrow through the program $5,500 as a freshman, $6,500 as a sophomore, and $7,500 as a junior and senior, totaling $27,000)
There are however private lenders (like the owners of College Confidential whose name I have obscured per TOS) that will offer loans without cosignors for significantly more incremental money beyond the Federal limits.
I don’t necessarily recommend taking on that incremental debt but it does exist as an option.
If however seeking I banking or consulting the debt may become inconsequential when spread across a more lucrative career that would be less accessible from non target but cheaper schools.