[marcomonteiro]

Actually that's (almost) exactly how I did it joining Apple. I had already interviewed and been turned down with the group I wanted to join twice. Now I was coming in for another interview with a different hiring manager. I was willing to put up with another possible rejection because I really wanted to work at Apple. So I worked with one of the recruiters and had setup interviews with 6 other groups. I did 2-3 interviews a week and it was grueling but in the end I had several groups that wanted to hire me including the original team I wanted to join. They could only make one offer but nothing stopped me from interviewing until I was blue in the face.

EDIT: Another note, at least three of the roles I interviewed for had homework assignments. None took longer than 2 hours and I actually enjoyed them and the subsequent interviews much better.