Flight Millage

I'm collecting flight millage from United, Northwest, and American. Even though I buy whatever cheapest tickets available, usually I can accumulate millage in one of those three because the rest of the airline companies affiliate with one of the three (except Soughwest, I sometimes fly with).

This time I bought tickets from Eva airline. The problem is that Eva is not affiliated with any of the three. Eva only goes with Continental even though Continental is affiliated with Northwest. So, I cannot earn millage of Northwest if I fly with Eva.

It seems like if I replace Northwest with Continental, I can cover more airlines, but the problem is that JAL only goes with Northwest, not with Continental.