If you visit other threads on this forum, you will find that MRI's, lesion loads and what they have to do with the mechanism of MS are insignificant.
For what it's worth, my past two MRIs have shown a reduction in lesions. The first reduction was shown after suffering on Avonex for nearly seven years, the second was after being on LDN for 9 months. On both occasions (different neurologists), I got some funky explanation suggesting that my case is but an analogy. (Funny, other people in the same situation have received similar reactions.)
All switching drugs will amount to is switching drugs. Because "the experts" (the FDA) say that MRIs are not an effective tool for monitoring disease progression, it's unreasonable to expect that any drug can effect lesion activity. If you're doing well on Copaxone, I would question your doctor what it is outside an MRI that makes him want to try a different treatment.
If you are concerned about the risk of Rebif damaging your health, but you get convinced that it's worth it, may I suggest getting some baseline data on your general vitals: CBC, enzyme count, blood pressure, physical ability, etc. After a reasonable duration (6 mos, 1 year, or more), check those vitals against your baseline. Use these results to decide if a drug is worth the risk.
First and foremost, I take care of my well-being. There are too many unknowns (and bad math) with MS for the "maybe" of a drug's efficacy to hinder my overall health. Remember, none of the approved medications is a "cure" for MS, nor have any shown 100% efficacy; therefore, they are all experimental.
How much of a guinea pig do you want to be?