How can a burned sugar caramel icing be doubled?

There is no reason a recipe like this can not be proportionally increased or decreased. Just figure out how much you need and adjust from there. So, in your example, increase everything by 1/3. ...but I don't see how doubling poses a problem.

I disagree with moscafj here, candy recipes are indeed tricky to scale. The reason behind it are heat gradients. And it doesn't mean that you can't do it, it just means that doing it is risky.

Sugar behaves quite differently at close temperatures, for example 114 C is soft ball and 118 is hard ball stage. Your pot gets heated from below only, and in the worst case also not evenly on the whole bottom, so you can have spots in the pot which are hotter than others. If you make a larger batch, it is deeper, and there is more temperature difference between the surface and the bottom. Especially if you make something which shouldn't be stirred, or should be stirred in a very specific way (fudge, some clear candies that can crystalize if stirred on the wrong time, or simple caramel with the dry method) you can find out that part of your candy has already overshot its temperature while another part is still underdone.

You can increase your chances of success if you use a wider pot, but it is good to also use a wider hob if available, putting a wide pot on a small hob will give you just the same problems. Also use a heavy bottomed pot that equalizes heat well, I prefer enamelled cast iron for my candy (but that introduces some other concerns like residual heat overheating the candy). The other thing that will help is experience with candymaking and understanding the basic principles - then you will be able to notice earlier if something goes wrong, and will know how to repair potential problems, and what not to do. If you are not at that level, you will have to jump in and try, even if it means wasting ingredients a few times. Reading on candymaking technology and doing courses with an expert will make the process quicker, but will not replace exercise.