How would I extend the JavaScript language to support a new operator?

The answer to the question Is it possible to create custom operators in JavaScript? is not yet, but @Benjamin suggested that it would be possible to add a new operator using third party tools:

It is possible to use third party tools like sweet.js to add custom operators though that'd require an extra compilation step.

I will take the same example, like in the previous question:

(ℝ, ∘), x ∘ y = x + 2y

For any two real numbers x and y: x ∘ y is x + 2y that is also a real number. How can I add this operator in my extended JavaScript language?

After the following code will be run:

var x = 2
  , y = 3
  , z = x ∘ y;

console.log(z);

The output will contain

8

(because 8 is 2 + 2 * 3)

How would I extend the JavaScript language to support a new operator?