Does transferring once diminish your chances of being accepted as a transfer into a UC?

the potential “gotcha” here is making sure you have enough units to be considered a junior. The UCs do not evaluate transfer credit prior to acceptance; they take it on faith you have the units you say you do and then check later. You can tell what CCC classes transfer from ASSIST, but its less obvious what gets credit from your current school. See http://admission.universityofcalifornia.edu/counselors/transfer/advising/transferring-credits/index.html

If you will be just over the border of 60 units it may be better to err on the side of caution and make sure you have enough total units.