Yes it is possible - I do that regularly (not just with RTWs). However, unless you fly a lot (say over 50k miles a year) it is probably not worthwhile diluting your benefits by spreading the miles across so many programs (especially within the same alliance).

You need to be a bit careful with this as can easily end up with miles in the wrong program, or missing out on some benefits of status because you have a lesser status FFP # recorded.