Thaumatolgy sorcery question

[Jaware]

I have a quick question that I'm not certain about.

I've read through the book twice and I didn't see anything written about it, though I may be mistaken, but I don't think it is addressed in said book.

I'm trying to find out if you can have alternate spells.

Like. I understand you have your main sorcery advantage. And it limits how big your other spells you can have are. And that you only pay 1/5th the price for the spells to "know" them.

My question is this.

Can you buy alternative spells to your spells?

For example. Say you begin with a sorcerer that throws 1d exploding fireballs for whatever the reason. After a bunch of sessions, you talk your dm into allowing you to up your damage to 2d fireballs. And maybe even 3d fireballs. So you calculate the additional costs from the previous versions etc.

But after wards, say you come into a situation where you want to cast a 1d fireball again for some reason. Do you have to "know" a separate spell to use a smaller fireball? And if so, can you buy it as an 'alternative firebal' to your full-size fireball?

Does anyone know off the top of their head?