TypeScript: ignore function signatures from inherited classes

Question

I'm trying to build an extension system with TypeScript. This system works as long as the extendable classes don't inherit from each other.

Here is a simplified version for this inheritance problem:

class ExtensionHost {
    addExtension(extension: Extension<typeof this>): void {}
}

class Extension<T> {}

class Object3D extends ExtensionHost {}

class Cube3D extends Object3D {}

class CubeExtension extends Extension<Cube3D> {}

class Object3DExtension extends Extension<Object3D> {}

const cubeExt = new CubeExtension();
const objectExt = new Object3DExtension();

const cube = new Cube3D();
const object = new Object3D();

cube.addExtension(cubeExt); // OK
cube.addExtension(objectExt); // Problem 1: should error, but doesn't

object.addExtension(objectExt); // OK
object.addExtension(cubeExt); // Problem 2: should error, but doesn't

The class Object3D is extendable. And the class Cube3D inherits this functionality from the Object3D. Yet I want to prevent it from extending any Extension that does not directly match its own class.

Problem 1: the cube should not be extendable with a Extension<Object3D>. By hovering over the cube.addExtension(objectExt) it gives me the call signature of Object3D.addExtension(extension: Extension<Object3D>).

Problem 2: the object should not be extendable with Extension<Cube3D>. Here it makes a bit more sense, because a Extension<Cube3D> is also a Extension<Object3D>. Yet it would still be nice to prevent it.

Question: Is there a way to type it in a way that those problems can be fixed on the type-level? Problem 2 is not that important.