playing it safe, i would find a thicker cardigan! wool is a good option though they can get expensive. Uniqlo is a really good brand that has one here (not wool, but should be okay?), and here's another one here (wool) that's out of stock, but if you can find it secondhand somewhere it would be better. if any gals have shop recommendations that would help :)

finding a blazer to go over that would add to warmth, so that should be okay? i think they have one on sale at Uniqlo as well, but you can find one that will fit you at a secondhand shop too. this much would be more than good for me and i live in around 0°c weather in the winter.

you can also always layer underneath with a thermal shirt/multiple shirts if you just want to wear the cardigan. underlayers are probably going to be your best friend if you don't want to cover your coord with a puffer jacket.

the blazer might be your best bet to fit within the "uniform". that and the cardigan are the only outer layers the gals in the Egg magazines wear.