Should A Person Be Able To Play Sport For More Than One Country???

Question

All in the Q Really.
The world really is a small place now.
A person can be born in one country, to parents who can be from two others & grandparents from a completley different 4.
Then they emmigrate somewhere else !!!
By most sports rules you can play for your country of birth, country of residence or parents/ grandparents counrty of birth.
If you have played for country A should you then for whatever reason (most common emmigration/ residency) then be allowed to play for B?
Surely representing your country should not be for personal success or glory - but pride, passion & 101% heart "for your country & the jersey" where you shed a tear whilst singing yor anthem.
Another point - Can a multi national player really be impartial?

Sorry, I don't mean representing two at same time I don't think any sport allows that.
But say you represent country A for a few years and are then eligle to play with country B (by residency, parental rights etc) or whatever
Either:
Country A are small & not rated in your sport but your new country B are bigger & better and you can change to B
OR
Your good at whatever you do and both your old (A) & new (B) country want you OR
You get dumped from country A but you could play for country B.

Answer 1

I dont think you should be allowed... it would cause arguments between the two countries that the player is playing for, because they could have matches at the same time and then the player would have to choose where his/her heart lies.

Answer 2

It depends on the rules set for by each nation's Olympic/sports federations. I don't have a problem with such rules, as long as they weren't "magically" written recently to stack a team for competition.