Here are my comments in no particular order:
Getting into an Ivy is a longshot for any unhooked applicant.
I suggest you look at the common data set for any school you are considering (google "common data set XYZ University) and check Section D to get statistics on transfer admissions.
Your CC should have a transfer advisor. Take advantage of his/her expertise.
I am also a bit nervous that anyone who continually clumps all of the “Ivy League” schools together is hunting for prestige over fit. The Ivy League is a sports league. While the colleges in the league are all excellent academic institutions they are very very different. For example, it is unlikely that a person who loves the idea of a big core curriculum like Columbia has would also want the unstructured curriculum of Brown; it is equally unlikely that a person who treasures the rural environment of Dartmouth would also want to be in an urban school such as Penn. I strongly suggest you research every school you apply to as a transfer student on its own merits.
And as I tell any applicant (transfer or freshman student) – work hard to create a well rounded list of transfer schools that includes some reach (Ivy and other top tier colleges) but also a good number of match a safety schools. There are tons of amazing colleges and universities out there – do the work to find the ones that are good fits for you.