That would yield an overlap for T = YourLocalTy. It's basically the same issue as with a non-inherent impl of a RemoteTrait: either the trait or the type would have to be marked #[fundamental] to express that such impls would not occur within semver-compatible versions.
In the meantime, I suggest that you use something like:
which greatly reduces the boilerplate of writing extension traits, hence yielding 95% of the ergonomics of inherent impls to begin with:
#[extension(trait MyLogic)]
impl<T, U> ForeignStruct<T, U, YourLocalTy> {
…
}