Recommended number of branches in sitemap’s hierarchy tree

We are working on a HUGE site with a current information architecture that is a mess, and we were asked to change as little as possible.

Just in case, the client understands that this is a mess and they understand that we will have to make some changes, they just want us to keep it to a minimum due to some important back-end concerns and the way they organized their work so far, based on this messy IA.

Context: this is for a website that works as an umbrella for many stores across the US, each one with its own specific branches. Users can access the site from the umbrella or from the store. In addition, the main site has a member area, and so does each of the stores, however, the type of member area in each of them is different.

Now, what we find is that the hierarchies in this IA are not very deep. In fact, it only reaches 5 depth levels (excluding multidimensional and external objects). But it's really huge in the horizontal view, which means you have MANY branches per level.

Although we will group many of them, I was wondering if there is any study or recommendation on the maximum number of branches for the hierarchy tree of a website.

Please note that visualization is not a concern for us, only the number of branches