Is there any way to extend an object?

As so often the correct answer depends on the actual business requirement. Extending from an object would in some sense defy the purpose of that object since it wouldn’t be a singleton any longer.

What might be a solution is to extract the behavior into an abstract trait. And create objects extending that trait like so:

trait T{
    // some behavior goes here
}

object X extends T

object Y extends T {
    // additional stuff here
}