My goal is to undertsand the actual implementation of the ImplicitRKMil algorithm here. Are there any notes or book sections directly relating to the code here?

The perspective of my question is this: I have a bunch of stiff SDEs where ImplicitRKMil with theta=1 (i.e. backward Euler) works best by far. However, it’s still not super stable, so I’m asking myself whether it would be possible to have higher-order implicit methods (in the sense that Euler is the simplest RK method)?

That does make a difference to an extent. SKenCarp should be better there, but yeah there aren’t that many methods focused on that domain and it would be nice to make some more.