Can pan reach level 4 saiyan

Yes, but only in Other World. This is because she is not strong enough to go super saiyan 4 like Goku and she can't even go Super saiyan 1. This problem is also because Akira Toriyama, creator of Dragon Ball, mentioned Pan would've been able to go Super saiyan, but he couldn't find the accurate design for her. It would've been even harder for him to think up a character design of super saiyan 4 pan, because she would've came out a blur or scribble. If she did though it would be really cool. She would have long, black hair, pink fur, her eyes would've looked serious, and her voice would sound deeper. So just thinking of SuperSaiyan4 Pan is cool!