Just to clarify, I contacted Amazon support and below is the answer I got. Looks like this feature could be available in the future.
I understand from your e-mail that you would like to have the following variation values for your listings: Style, Size, and Color like ASIN: B07BKGJ786.
Please note that only Amazon retail and Vendors has the ability to create variations with three Variation dimension theme currently. If you see any of such variation on our catalog, it is because Amazon retail / vendor has created the variations for it. I can see that the ASIN: B07BKGJ786 was created by our retail team because which it has three variation values.
I would like to inform you that having a variation theme with three variation values is not possible for your listing.
I sincerely appreciate your efforts in trying to add this variation theme to enhance the customer experience by providing them more options while selecting your product. However, I regret to inform you that this option is not available at this time to ASINs that are not created by the retail team or vendors.
However, this does not mean that this option will not be available in the future. I have considered exception like in this scenario as the feedback and have already forwarded your interest to our dedicated specialists’ team and our team is already working on this so that they can avail this option to our sellers in the future. We don’t have a specific time frame as to when this option will be available but when this feature is launched, you will be notified through your seller central account.