Here is a link to a study from 2009]
www.ncbi.nlm.nih.gov/pmc/article ... ool=pubmed[/url].
Although the results of the study do show that doing 2 aways has statistically higher match rates, 3 aways is not far behind at all. The study also went on to break down the type of applicant who does 2 versus 3 or more aways, showing that the typical applicant doing 3 aways is a weaker applicant.
So as far as I can tell, if you are a strong applicant (Scores, grades, LORs, research, etc), doing 3 aways should only HELP you. The 3rd away would most likely be late enough in the year that ERAS +/- Dean's Letter already went out, so it should only help/hurt you at that specific 3rd program (i.e. you won't be counting on the LOR from a 3rd away to improving your app to all other programs).
However, this is a bit different if you do not plan to or have the option to rotate at your home program before going on aways. If I were you I'd definitely do 3 aways.