Try applying to smaller companies. Smaller companies aren't going to land the candidate from a top 10 school who already interned at multiple Fortune 500 companies. But small shops need to hire talent too. They're digging deeper and they have to read the resumes more closely. There isn't much of an HR department, and the hiring manager might be sifting through the raw resumes themselves.
If you still want to land a big company job, you're going to need to bypass the HR filter by finding a direct line to the hiring managers. Maybe you have some friends or alumni you've met who are at the company and can refer you directly to a team. You can meet these people at networking events, recruiting fairs, or other social activities. Creativity, determination, and luck play a big factor.