> Can somebody, anybody, then please answer how we deal with functions that vary independently of the region index (or indices)?

I don't really get your problem as saturation functions (and thus endpoint scaling if I understood EPS, correctly) are independent on PVT properties, right? one of the few exceptions are the  phase mobilities which can be calculated like this

```c++
void mobilities(inputs, outputs)
{
   calculateKr(satnumOfCell, ...); // <- EPS used here?!
   calculateViscosity(pvtnumOfCell, ...);
   // multiply kr and mu
}
```