Comment by the_af

Challenge accepted.

    from dataclasses import dataclass
    from typing import Protocol, Self, TypeVar

    class Semigroup(Protocol):
        def __add__(self, other: Self) -> Self:
            ...

    T = TypeVar("T", bound=Semigroup)
    def join_stuff(first: T, *rest: T) -> T:
        accum = first
        for x in rest:
            accum += x
        return accum

    @dataclass
    class C:
        x: int

    @dataclass
    class D:
        x: int
        def __add__(self, other: Self) -> Self:
            return type(self)(self.x + other.x)

    @dataclass
    class E:
        x: int
        def __add__(self, other: Self) -> Self:
            return type(self)(self.x + other.x)

    _: type[Semigroup] = D
    _ = E

    def doit() -> None:
        print(join_stuff(1,2,3))
        print(join_stuff((1,), tuple(), (2,)))
        print(join_stuff("a", "b", "c"))
        print(join_stuff(D(1), D(2)))
        print(join_stuff(D(1), 3))
        print(D(1) + 3) # caught by mypy
        print(D(1) + E(3)) # caught by mypy
        print(join_stuff(1,2,"a")) # Not caught by mypy
        print(join_stuff(C(1), C(2))) # caught by mypy
    doit()

Now, this doesn't quite work to my satisfaction. Mypy lets you freely mix and match values of incompatible types, and I don't know how to fix that. Basically, if you directly try to add a D and an int, mypy will yell at you, but there's no way I've found to insist that the arguments to join_stuff, in addition to being Semigroups, are all of the compatible types. It looks like mypy is checking join_stuff as if Semigroup were a concrete class, so once you're inside join_stuff, the actual types of the arguments become irrelevant.

However, it will correctly tell you that it can't accept arguments that don't define addition at all, and that's better than nothing.