Identify [or restrict] if a class’s method was called from another instance of the class

I have a class with a private data store, in a custom format. I have made the data store private, so that people will work with the API and not directly mess with the underlying structure.

I want to implement a merge method, that will allow one instance of my class to merge into another. To make this performant, the merge function needs access to both instances’ data stores.

class MyClass() {
  #myDataStore; // custom data structure that i don't want people messing with. (private)
  ...
  mergeDataStores(instance2) {
    const dataToMerge = instance2.#myDataStore; // !IMPORTANT! - this what I want to be able to do
    ... // perform the actions needed to merge the two.
  }
  ...
}

const instance1 = new MyClass();
const instance2 = new MyClass();
... // various actions that load data into instance1 and instance2
instance1.merge(instance2);

is there any way I can accomplish this without exposing my data store?

Solutions that I don’t know how to implement, if they are even possible

1. Is it possible to have an access modifier (aka another option for what other languages would call public, private or protected) that means “this value can only be accessed by an instance of the same class”?
2. In a method, is it possible to check the instance of the class that invoked the method? That would let me create a getter that checks if (!(invokingContext instanceof MyClass)) throw new Error("Access denied!");

Am I missing another option?