Inclusion of higher-order terms may obviate the need for such a correction, thus the present work is an effort to implement energy screening in a general way at all orders of MBE(n). We describe a new "bottom-up" algorithm, by means of which an arbitrary screening procedure may be extended from low-order to high-order n-body subsystems, for arbitrary n, without the need to define bespoke screening algorithms for different nbody levels. The bottom-up algorithm is demonstrated in applications using MBE(n) up to order n = 8, making use of a new software application in which MBE(n) is tightly integrated with the semi-empirical extended tight-binding (xTB) model. This replaces the polarizable force field that was used previously as the low-level screening method, and represents a much more flexible and general means to screen the low-order subsystems.