Update 3/2022
There is currently a proposal to add Records and Tuples (basically immutable Objects and Arrays) to Javascript. In that proposal, it offers direct comparison of Records and Tuples using === or !== where it compares values, not just object references AND relevant to this answer both Set and Map objects would use the value of the Record or Tuple in key comparisons/lookups which would solve what is being asked for here.
Since the Records and Tuples are immutable (can’t be modified) and because they are easily compared by value (by their contents, not just their object reference), it allows Maps and Sets to use object contents as keys and the proposed spec explicitly names this feature for Sets and Maps.
This original question asked for customizability of a Set comparison in order to support deep object comparison. This doesn’t propose customizability of the Set comparison, but it directly supports deep object comparison if you use the new Record or a Tuple instead of an Object or an Array and thus would solve the original problem here.
Note, this proposal advanced to Stage 2 in mid-2021. It has been moving forward recently, but is certainly not done.
Mozilla work on this new proposal can be tracked here.
Original Answer
The ES6 Set object does not have any compare methods or custom compare extensibility.
The .has(), .add() and .delete() methods work only off it being the same actual object or same value for a primitive and don’t have a means to plug into or replace just that logic.
You could presumably derive your own object from a Set and replace .has(), .add() and .delete() methods with something that did a deep object comparison first to find if the item is already in the Set, but the performance would likely not be good since the underlying Set object would not be helping at all. You’d probably have to just do a brute force iteration through all existing objects to find a match using your own custom compare before calling the original .add().
Here’s some info from this article and discussion of ES6 features:
5.2 Why can’t I configure how maps and sets compare keys and values?
Question: It would be nice if there were a way to configure what map
keys and what set elements are considered equal. Why isn’t there?Answer: That feature has been postponed, as it is difficult to
implement properly and efficiently. One option is to hand callbacks to
collections that specify equality.Another option, available in Java, is to specify equality via a method
that object implement (equals() in Java). However, this approach is
problematic for mutable objects: In general, if an object changes, its
“location” inside a collection has to change, as well. But that’s not
what happens in Java. JavaScript will probably go the safer route of
only enabling comparison by value for special immutable objects
(so-called value objects). Comparison by value means that two values
are considered equal if their contents are equal. Primitive values are
compared by value in JavaScript.