Can I intercept/trap object behavior on comparison for equality

Question

Playing around with Javascript objects is fun, and annoying:

const MyObject = function(value)  {
  let _myObject = {
    [Symbol.valueOf]() {
      return value
    },
    [Symbol.toPrimitive]() {
      return value
    },
  }
  return _myObject
}

let o = new MyObject("a")
let p = new MyObject("b")

o == "a"
# true

p == "a"
# false

o < p
# true

p < o
# false

p + "-foo"
# 'p-foo'

Having custom objects behave like primitive types looks potentially useful and intuitive! Until you try something like this:

let o = new MyObject("a")
let p = new MyObject("a")

o == "a"
# true

p == "a"
# true

o == p
# false

Javascript will (quite sensibly) return false when comparing two objects for equality.

Would there be any way to hack around the apparent “inconsistency” arising in a case like this? (Maybe some clever usage of proxies/Proxy handlers? )