I feel its possible. I see purpose as that one area of life's vacuum we were made to fill. However, it would seem that some people are made to fulfill more than one purpose, like be the husband of a lady while still being the richest man in the world.
Some people do find fulfillment doing more than one thing. I think that can be akin to finding purpose.
SOME people have the purpose of being the president of a country while still playing golf. It happens like that.
I'm by no means authority in this but it is my candid opinion that it is possible.
In Christianity, we believe that there are two purposes for everyone. There is the generic and then the specific.
We believe that every believer has been called to preach the gospel of reconciliation. That is the generic purpose but we also believe that everyone , I mean every single person, has a purpose that only he/she can fulfill.
So, whatever your belief, it's possible to have two purposes.