The headquarters of Pixar and Lucasfilm are located about 24km apart in Northern California. Both companies are also owned by Disney. Those factors would make it seem like some kind of team up is inevitable, and yet, each is doing just fine on its own. However, if they were to collaborate, the result may look something like this.
What you see here is a fun piece of fan art by artist Mark Chilcott called Pixar Wars, and it speaks for itself.
Edna Mode as Darth Vader, Elastigirl as Princess Leia — just perfect. Of all the character mash-ups, though, I think Kylo Ren Syndrome is the most spot on. Unlike Sully and Chewbacca, or Carl and the Emperor, Kylo and Syndrome are very, very similar as characters. OK, Mike and Yoda too.