I'm not sure whether completing a foreign pre-defined story would work out well...
A friend of mine already tried to push me into writing a dual-story (two authors writing chapters individually), but we didn't make it past the first few pages...
Its not like dual story writing.
Only if you need some inspiration about a new world and stuff.
I'm not working on it anymore and also not planning on doing it in the future but maybe its usfull for your new story?