Changing variant once per frame via code

I have an object with a big amount of variants and variant sets.
I would like to create one frame for each permutation of variants.

I have been able to iterate all permutations, but I am not sure I understand how to create a keyframe that allows me to have a single frame with each permutation of materials.

Default animation curves only have specific prim properties like position, rotation etc, i’d like to apply a specific variant instead.

is there some reference on how I could do this ?

Or, is there some other way I could achieve the same result ?
thank you again

Let me see if I can find someone to help you on this