Suppose I apply a PRF to a secure MAC. Do I still have a secure MAC?
A secure PRF is a secure MAC. A secure MAC of a secure MAC is a secure MAC. Therefore, applying a PRF to a MAC still gives you a MAC.
Depending on the length of the inner MAC and the PRF you may lose security bits, but if they are long enough it works.
Assuming you're asking if PRF(MAC) can be used as MAC (message authentication code)? Depends on the PRF. MAC is de-factor PRF too with several properties in mind (collision resistance, pre-image resistance, avalanche effect, non-linearity...).
Until your PRF keeps these properties, you should be ok. The basic idea is you should not weak the strength (length) of the MAC.