To compute DEE for an MPS

I wanted to calculate the disconnected entanglement entropy for S=\frac{1}{2}, N spin chain.

S_D^{n} = S_A^n + S_B^n - S_{A\cup B}^n - S_{A\cap B}^n

where

S_D^{n}

is Entanglement Entropy (n=1; is von Neumann entropy) for a disconnected region D
A,B denote two regions, suppose I have N = 8 sites, then A = {1,2,3,4} and B = {3,4,7,8}.
To calculate entanglement entropy for A is trivial using ITensorEntropyTools.jl, can anyone suggest me a way to find the entropy for the discontinuous region B

You can just pass the sites with that package as well

ee_region(p, [3,4,7,8])

That will scale exponentially with the size of B though, so potentially using something like movesites (movesite) could pay off in some cases at the cost of a higher bond dimension (also exponential in cost).