I transferred from a CCC to UC Berkeley as a Philosophy major in 2016, and I’m now gearing up to apply to PhD programs in Philosophy. I’m not sure whether this advice applies to PhD programs across the board, but if you want to be a Philosophy professor, the prestige of your undergraduate institution is extremely important (at least for analytic philosophy, and probably for continental philosophy as well).
If you plan to transfer to a school that is not ranked on the Philosophical Gourmet Report (http://www.philosophicalgourmet.com/overall.asp), which is the authoritative rankings of Philosophy departments, you should reconsider. (There are some exceptions - it’s well-known that Reed has an excellent Philosophy department, but they don’t have a graduate program, I think, so they aren’t included in the PGR rankings.)
This is because professional philosophy is extremely elitist. Famous professors at top schools all know each other, and trust their opinion - so an applicant whose letter of recommendation writers are well-known professors is likely to be accepted over an applicant whose letter writers are not well-known. Moreover, suppose you do go to a PGR-ranked school, and you apply to school X. If someone on the admissions committee at school X knows one of your letter writers, they might give your professor a call to ask about you. I’ve been told by my professors that this happens pretty often - and here, too, going to a top institution and getting close with top professors proves to be very useful in your application. Letters of recommendation are a huge part of the PhD application, so all of this is really important to keep in mind.
A philosophy professor at UCR said, “To my knowledge no UCR undergraduate has ever been admitted to a top-15 philosophy Ph.D. program (certainly not in the 10 years I’ve been here), though we’ve had some students with straight A’s, very strong letters, and excellent writing samples” (http://schwitzsplinters.blogspot.com/2007/09/applying-to-philosophy-phd-programs.html). This is not to say that, if you go to a non-PGR ranked school, you won’t get into a top school; one of my CC professors went to UC Davis, and then got his PhD at MIT. But it is much more difficult to get into a top school if you’re not already coming from a top school.
Also, when you apply to PhD programs, you want to have the best writing sample you can. It is extremely helpful to be close enough with well-regarded professors that they will help you with your writing sample. Generally speaking, these professors are well-regarded because they’re good at philosophy, so working with well-regarded professors will help improve the quality of your writing sample. (It is fine to work with professors who are not as well-known, of course, if you are comfortable with them, and their writing is good. But it is seriously advantageous to work with people who are leaders in their field.)
I wish I knew how political and elitist academic philosophy was before I even applied to transfer from CC (not that I regret it, I love it of course!) Bottom line, if you want to get a PhD in Philosophy, it would seriously improve your chances to transfer to a top 10-20 PGR-ranked school (ideally UC Berkeley and UCLA, but UCSD, UCI, and UCR have strong analytic philosophy programs as well.)