Hi Jason,
From what you have posted, it seems to me (and I'm not a doctor), that even though you have been and still are on Avonex, apparently you are having "breakthrough disease activity", even while on an interferon.
Tysabri is 68% effective at preventing further relapses, slowing the disease process down, and in some patients-even showing symptom improvements. The efficacy's of Avonex, Betaseron, Copaxone, & Rebif are only 34% to 27%, respectively.