Vegeta doesn't have as many transformations as Goku, but that's simply because the Prince of All Saiyans doesn't need them.

Dragon Ball Daima revealed that Vegeta had indeed also unlock the Super Saiyan 3 form rather than seemingly skipping over it as teased by the future events seen in Dragon Ball Super, and this form ...

So far in Dragon Ball Daima, we’ve seen both Goku and Vegeta transform into Super Saiyan levels one and two, with the Saiyan Prince revealing his Super Saiyan 3 transformation for the first time.