has it ever ranked among the top institutions?
Yes.
Florida International University
For 2020, "U.S. News & World Report" ranked Florida International University as the 105th best public university in the United States, and 218th overall among all national universities, public and private.

what part of florida is florida international university University Park, Miami. when was this university established? 1965. by whom? W. Haydon Burns, the Board of Education and the Board of Regents. was there any government university there before this? No. was the university expanded later? Yes, into the Herbert Wertheim College of Medicine, the FIU College of Law, the FIU School of Architecture and the Robert Stempel School of Public Health.
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Florida International University [SEP] Rankings
For 2020, "U.S. News & World Report" ranked Florida International University as the 105th best public university in the United States, and 218th overall among all national universities, public and private. In 2010, FIU was listed as one of 16 universities with the toughest grading system nationally. In 2000, FIU became the youngest university to be awarded a Phi Beta Kappa chapter, the country's oldest and most distinguished academic honor society. FIU is one of only 78 universities nationwide to hold both designations.