I agree with kubiiii.

Since a rewrite is in the card (hopefully) there is something wrong with the entire system.

* Identify where the applications interact with each other.

* Identify the most problematic applications.

* Rewrite those (starting with the smallest) while trying to keep the interfaces between applications constant.

And involve end users as much as possible.

Why not (sounds easy eh?) go one application at a time? Are there interactions between apps? Maybe you can start with documenting all the interaction (~ api). Then you'd go deeper in each app.