Update NumericalFunction in NDSolve

Question

I have NDSolve` StateData from an NDSolve` ProcessEquations evaluation. I can NDSolve` Iterate from t0 to t1, but then my boundary condition (an interpolation function) runs out of data.

This interpolation function gets updated externally. I just want to continue iterating (t1 to t2) with the updated interpolation function. However, calling myStateData@"NumericalFunction" shows that NDSolve holds onto the old interpolation function, even though this function is defined with a delayed set i.e. myInterpFunction[t_]:=something[t]

Is there any way to update the functions inside of the state data?

Here is a simplified version of what I'm doing:

myStateData = NDSolve`ProcessEquations[
    {myPDE[x,t],
    (*boundary conditions*)
    T[xf, t] == myInterpolationFunction[t],
    T[0, t] == 0,
    (*Initial condition*)
    T[x, t0] == initialCondition[x]};
    T, t, {x, 0, xf}]

Then I need to solve so...

NDSolve`Iterate[myStateData,t1]

Then externally I update my boundary condition so that now it goes to t2 but when I evaluate

NDSolve`Iterate[myStateData,t2]

Mathematica returns an error saying that the interpolation function doesn't cover that range (t1 - t2) because it's holding onto the old interpolating function. In other words, looking at

myStateData@"NumericalFunction"

shows myInterpolationFunction has a domain of {t0,t1}