Drugs not working

My partner was started on Copaxone following a big hit that took out his left handside, which he appeared to fully recover from within a month, but then had a full right side relapse, so was then swapped to Betaferon. Sadly yet another relapse, mainly affecting his legs so they are going to do an MRI scan and there is talk of changing his medication again. This time although the relapse was less severe, as he was able to continue with life to a degree it has taken much longer to recover and he is only about 80% of what he was.

Does this mean that he is moving from RR to progressive MS? What other medication is available if the above drugs failed?

First, it is quite possible to be RRMS but make an incomplete recovery from relapses. In a really brutal relapse there can be damage that is not reparable. Sad experience speaking here.

Second, your partner has been on the first-line DMDs - they are the safest ones that are the ones they tend to try first. But here are stronger drugs available if the first-line drugs fail. Your partner is not out of ammunition yet - there are stronger drugs in the locker if those are needed.