In other words, (assuming the current class hierarchy) why not just have:
```python
class Interpolator(...):
    def __init__(self, cube, interp_coords):

class LinearInterpolator(...):
    def __init__(self, cube, interp_coords, extrapolation_mode='linear'):
        self.extrapolation_mode = extrapolation_mode
        super(LinearInterpolator, self).__init__(cube, interp_coords)
```