No it doesn't. I think the intention behind Super Saiyan Blue was that Goku and Vegeta had mastered Super Saiyan, making it inherently better than Super Saiyan 2 and 3. And by doing so, they managed to infuse it with their God-Powered Base to reach Blue. Obviously this changed because Saiyan Beyond God but I think the point still stands. Super Saiyan is the only form they had mastered which allowed them to combine it with God to obtain Blue. I don't think Super Saiyan Blue 2 is a thing or even possible for them.
The manga makes a clear point that Goku had reached a wall that couldn't be overcome through sheer power. The anime makes it a point that Goku pushed himself way beyond his limits to obtain Ultra Instinct Omen. Likewise, Vegeta pushed himself beyond his limits which led to an Evolved form of Blue. Besides, with Ultra Instinct and Ultra Ego, it kind of renders the point of SSJB2 anyways.
Whatever we see from Goku is just an animation error.