As stated elsewhere, e.g. in German language Aerotelegraph, only three recommeding airlines are necessary and benefits such as status miles or lounge access only apply to those.

I think this makes sense, since a common complaint of all alliances was that some hardly connected members doesn't make too much sense commercially. E.g. JAL joining was one of the reasons for EI to leave, because of significant adaptation cost and limited commercial benefits. I think this would even be worse in case of Fiji, which probably have QF, BA and ??? as a partner.