Yes. Its very common, hence the different studios around the world. Another thing that happens quite a bit is farming out a design to a competing company. Nissan/Renault did this with the G35 coupe....they wanted a really cool design, the let their in house design studios around the world do it, but they also hired other design studios (often called design consultants...ie, Frog Design, IDEO, Pininfarina, The Fuse Project, DesignWorks (BMW)).
With the G35, the winner happened to be Porsche. Yup, you heard me. Porsche designed the G35 coupe...not Nissan, not Renault. They pretty much won the "competition". Its similar to what happens in the military industry....air force asks Boeing, Lockhead Martin, Northrop and etc. to come up with the next "whatever"...the winner gets the contract.
So in this case, Nissan was like "Well...we want to sell alot of these...Porsche's design was better than ours, so we'll use their design (that we hired them to do) to produce the G35 coupe."
Another example is Pininfarina. Honda hired them in the past to do a concept design. I forgot what it was called...it was the black/chrome Honda concept car.