A way to subclass NamedTuple for purposes of typechecking

The way named tuples are constructed make inheritance from typing.NamedTuple classes as yet not possible. You'd have to write your own metaclass to extend the typing.NamedTupleMeta class to make subclassing work, and even then the class generated by collections.namedtuple() is just not built to extend.

Instead, you want to use the new dataclasses module to define your classes and achieve inheritance:

from dataclasses import dataclass

@dataclass(frozen=True)
class Base:
    x: int
    y: int

@dataclass(frozen=True)
class BaseExtended(Base):
    z: str

The module is new in Python 3.7 but you can pip install dataclasses the backport on Python 3.6.

The above defines two immutable classes with x and y attributes, with the BaseExtended class adding one more attribute. BaseExtended is a full subclass of Base, so for typing purposes fits the requirements for the DoSomething() function.

The classes are not full named tuples, as they don't have a length or support indexing, but that's trivially added by creating a baseclass that inherits from collections.abc.Sequence, adding two methods to access fields by index. If you add order=True to the @dataclass() decorator then your instances become fully orderable the same way (named) tuples are:

from collections.abc import Sequence
from dataclasses import dataclass, fields

class DataclassSequence(Sequence):
    # make a dataclass tuple-like by accessing fields by index
    def __getitem__(self, i):
        return getattr(self, fields(self)[i].name)
    def __len__(self):
        return len(fields(self))

@dataclass(frozen=True, order=True)
class Base(DataclassSequence):
    x: int
    y: int

MyPy will soon support dataclasses explicitly; in version 0.600 you'll get errors still as it doesn't recognise the dataclasses module import or that a __new__ method is generated.

In Python 3.6 and earlier, you can also install the attrs project to achieve the same effects; the above sequence base class looks like this using attrs:

from collections.abc import Sequence
import attr

class AttrsSequence(Sequence):
    # make a dataclass tuple-like by accessing fields by index
    def __getitem__(self, i):
        return getattr(self, attr.fields(type(self))[i].name)
    def __len__(self):
        return len(attr.fields(type(self)))

@attr.s(frozen=True, auto_attribs=True)
class Base(AttrsSequence):
    x: int
    y: int

dataclasses is directly based on attrs, with attrs providing more functionality; mypy fully supports classes generated with attrs.

There is PEP 544 that proposes an extension to type system that will allow structural subtyping (static duck typing). Also runtime implementation of typing.NamedTuple will be improved soon, probably in Python 3.6.2 end of June (this will be also backported via typing on PyPI).