Please note that I am making no judgments w/r/t educational quality, only odds of admission.
First, look at state schools. Almost invariably you have your best odds of acceptance in-state (with the possible exception of ultra-competitive California). Otherwise, some schools that have traditionally been considered private alternatives for applicants unsure about their credentials are Drexel, Rosalind Franklin (formerly Finch), New York Medical College, Meharry, Creighton, Virginia Commonwealth. Tulane is known for recruiting individuals with unique interests or a compelling "total package" despite a weak academic record or other "standard" blemishes. This is not a complete list and earning acceptance to one of these schools is in no way "easy" -- in fact, the number of applications to these places are surging due to less self-selection than more competitive institutions, resulting in a comparably low acceptance rate. The big difference comes from the numbers-- at these places you can get by with lower GPA/MCAT and a less glowing application overall.
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