"Vielleicht wird er mir auch noch meinen nächsten Wunsch erfüllen."
It means 'another' here, as in 'additionally' or 'on top of' what's already been said. 'noch', especially with the help auf 'nächsten' says he has already fulfilled your wish and you're hoping for more. 'noch' is an emphasis, saying: He did it once, he might very well do it again. Without 'noch', 'nächsten' alone could mean the same minus the emphasis, but 'noch' stresses your first fulfilled wish more. Both would be understood, in my opinion, so it might be up to the speaker and their intentions. How about: Maybe he will also fulfill another of my wishes. Not as literal, but making use of the emphasis. Does that work for you?
It leans towards 'noch einmal', in my opinion, without being literally that. The redundance is what forms the emphasis really, it puts the weight into a certain direction, similar to 'yet another', where yet just underlines that there has been similar before and now there's even another.