This was, at its core, a production mistake. Goku and Vegeta were originally going to have just Base and SSBlue; then they were given Base, Yellow-haired forms again, and SSBlue. However, confusion arose among the fans as to whether or not Goku and Vegeta had a Black-haired Base form weaker than their SS1 forms AND a Black-haired Base form above all their Yellow-haired forms but below the Blue form.
Things changed again. Now Goku and Vegeta have Base, the Yellow-haired forms, the Red-haired form, and the Blue-haired form. But where did the strong second base go? It was assumed by 99% of the community that it was retconned into non-existence. I was part of the 99% and just accepted this.
Recently, I saw a drawing by Masaki Sato of his interpretation of an Ultimate Goku form, based on Ultimate Gohan -- it looks just like Base Goku. This drawing coupled with DBSuper acting like Ultimate is a transformation gave me an idea:
In my own world, and my own headcanon, Goku and Vegeta were using the Ultimate transformation during these moments of going "Saiyan Beyond God." So during the fight with Frieza, Copy-Vegeta, Monaka-Beerus, and others, Goku and Vegeta were tapping into the Ultimate form. This makes some sense because the strength of the Saiyan jumps by a large quantity when accessing Ultimate e.g. Gohan's cases. Ultimate also would hypothetically not change the look for Goku and Vegeta, which explains people thinking it were a second base. Their ki can also be felt in this strong second base form, and ki is felt normally when a Saiyan is in Ultimate.
So ... in my own headcanon world, in order to create a holistic explanation of the 131 episodes of DBSuper without resorting to an out-of-universe retcon, Goku and Vegeta have access to Base, SS1, SS2, SS3 (not Vegeta), Ultimate, SSG, SSBlue, SSBlue KK/SSBE. We know that Ultimate can be unlocked by Old Kai, but in this, I'm assuming it can be done by any God or Angel. Perhaps Whis gave them assistance in this.
Thank you all for considering this headcanon idea. I am not trying to push this as a fact or force the theory on anyone; however, comments and responses are welcome.
![Smile :)](./images/smilies/icon_smile.gif)