Are there "Buscher rules" for S-duality?

Question

I'm studying T-S-T dualities, and in particular, I'm looking at the example of the TST black hole in https://arxiv.org/pdf/hep-th/9601130v2.pdf 

My academic background is in T-duality, so I'm familiar with the usual Buscher rules for performing T-duality along the direction of an isometry, but I have no idea how to do S-duality. Indeed, I have very little idea of what S-duality is, other than a vague handwaving notion that it is a duality of IIB which inverts the coupling constant. In order to understand TST dualities, I'd like to do some calculations, and so I was wondering how one performs S-duality on a general background. Are there Buscher-like rules for S-duality?