Python: Can a subclass of float take extra arguments in its constructor?

As float is immutable you have to overwrite __new__ as well. The following should do what you want:

class Foo(float):
    def __new__(self, value, extra):
        return float.__new__(self, value)
    def __init__(self, value, extra):
        float.__init__(value)
        self.extra = extra

foo = Foo(1,2)
print(str(foo))
1.0
print(str(foo.extra))
2

See also Sub-classing float type in Python, fails to catch exception in __init__()

Both @cgogolin and @qvpham provide working answers. However, I reckon that float.__init__(value) within the __init__ method is irrelevant to the initialization of Foo. That is, it does nothing to initialize attributes of Foo. As such, it rather causes confusion on the necessity of the operation toward subclassing the float type.

Indeed, the solution can be further simplified as follows:

In [1]: class Foo(float):
   ...:     def __new__(cls, value, extra):
   ...:        return super().__new__(cls, value)
   ...:     def __init__(self, value, extra):
   ...:        self.extra = extra

In [2]: foo = Foo(1,2)
   ...: print(str(foo))
1.0

In [3]: print(foo.extra)
2