3rd SAT

My first SAT score was 2020 with
Maths - 710
CR - 570
Writing - 620
And with Erica Meltzer’s grammar book and practice tests I got a neat 2210 in my second SAT
MATHS - 750
WRITING - 790
CR - 670
But the predicament lies in the fact that I’m an international student and the competition is rigorous(which is an understatement). Plus I am acquainted with the mistakes I made in CR and am very confident that I can cross 750 in CR. Also I’m planning to apply early action to UChicago which has its 75th percentile CR at 800!
So would it hurt my chances if I give SAT for the third time, and say get a perfect score(which I believe is completely feasible.
Thanking you in advance.
And by the way, my extra curricular and academics are pretty much up to mark.