Background required for the book by Brigo and Mercurio

My aim is to be able to read and understand almost all of the book by Brigo and Mercurio including HJM, LMM and the Local Vol models. So that I am able to implement these models on my own. My question is what background do I need to be able to do this?

I have read Rannie and Baxter as an introduction to Stochastic Calculus and am now reading the book by Shreve. Do I need to read anything else after Shreve as a preparation or will it be sufficient? I am happy to read and put in the hours, as long it helps me understand and master Brigo and Mercurio and then more advanced books on this topic as well.

You can start to understand Brigo and Mercurio from the standard Shreve material but it does not look at things from the perspective of semimartingales which will possibly be confusing at some point. You're probably going to want to understand $d[X,Y]_t$ quadratic variation notion vs just the whole "$(dW(t))^2 = dt$" concept from the Shreve book that I'm assuming OP is referring to. Shreve wrote another excellent book Karatzsas and Shreve, Brownian Motion and Stochastic Calculus with the follow up Methods of Mathematical Finance both of which I can absolutely recommend as being challenging but amazing to learn from, something like "blue rudin" at times.