By rules as written, no. Extra Evolution requires the Eidolon class feature, which Primal Companion Hunters don't get. They have the ability to give their animal companion evolution points, but that feature is called Primal Transformation, not Eidolon.
Of course, your GM might allow you to take Extra Evolution. Just make sure you don't optimize your companion too much. I've never played a Summoner, but I get the impression a well-built Eidolon can trivialize encounters or overshadow other characters. That fits with my experience the one time I got to see one used.