Indeed, there haven’t been any models of 12 Grimmauld Place as of yet, and even though the house features in a number of memorable scenes in the movies, even those scenes have never been depicted in an official LEGO model since the inception of the theme 20 years ago. I am still keeping my hopes up this will be a set, perhaps even including the folding motion to make it appear magically! One can only hope ....
It is actually quite common to turn official LEGO models into alternate builds, even if the set is not an official 2-in-1 or 3-in-1 model. This is called a MOD (covered in this question here on this site). A famous one in the AFOL world is the MOD that turns 10214 Tower Bridge into a proper Modular Building.
There are several websites that feature MOD designs. The best known one is Rebrickable, where AFOLs can upload designs for any set (including MODs) and allow people to match up the pieces in their collection to the design, sell the instructions etc.
Another well-known site is Eurobricks, where scattered throughout the vast amount of forums and threads you can search for [MOD] in a posting title and find a lot of examples of MODs.
Back to the question: To make 12 Grimmauld place you need a set with lots of windows, 1xN bricks and a door. Looking at what sets are currently available, I think set 75980: Attack on the Burrow is a good candidate.
As you can see, it has lots of bricks including masonry profile bricks, as well as windows and a door.
I went ahead and tried to build 12 Grimmauld Place. Here is what I built using only pieces from 75980. Did I come close enough?