Contested boundary states - multiple BCs per boundary

[xtalax]

I will preface this by saying that method of lines at heart is about creating a unique equation to match every unknown state in the discretized grid.

Imagine discretizing a 2D system with 2 boundary condition equations per interface.
At present all boundaries are treated equal, so for the below 5x5 domain after discretization there are 6 equations per interface, not including corner equations:

cBBBc (c = corners, B = uncontested bc1, 
BxbxB  b = uncontested bc2, 
BbIbB  x = contested between interfaces,
BxbxB  I = interior)
cBBBc

This means that there will be competition for the states marked x. We clearly need to drop some corner equations to ensure balance for this discretization, but which ones?
Preferential treatment of an interface would lead to artificial asymmetry in the discretization, which we don't want.

What heuristic would be best with this solution?

Creating hybrid equations for the contested points would be difficult for me to do without some more insight in to rerarranging equations in symbolics, and may not be possible to do in general.

I'd appreciate your intuition as to the least bad way to go about solving this @ChrisRackauckas @YingboMa.