I don't believe that it is a requirement of either major alliance to sever ties with any competing airline.
Singapore owns a large stake in Virgin Atlantic (either 49% or 51%, I forget exactly). Virgin currently has no official plans to enter Star, which SQ is a member of. Virgin could hypothetically enter it, but I don't think it will happen: Virgin needs to steer clear of major alliances, or else it would kill their "NO WAY BA/AA" arguments (no one likes a hyptocrite, especially the government!
http://www.flyertalk.com/forum/smile.gif).
One thing is clear, though: Until the demise of ANA, we won't see JAL in the Star Alliance. Talk about domination in Japan!