Wrong, it does get special abilities at each +, +1 has magic attack 2, at +5 it might get something additional to just magic attack (like AP regen granted for all one knows)
I already had a +1 Sage staff, the bonus stat is "magic attack 2" (which can lead one to believe that a +5 would have "magic attack 15").
Yes I said had, it was vital with two vital bases, so I dismantled it and got a vital base and a magic base, so now can make a magic type +1 when I get my 4th recipe. (Technically 3rd, I guess now)