How to shuffle specific set of elements in a list?

I have created an ArrayList<MyObjects>. MyObject has an attribute priority, and implements the comparable method, which I have overriden.

I want to:

Sort ArrayList<MyObjects> based on the priority attribute. I've done that with:

Collections.sort(ArrayList<MyObjects>)

BUT, after the sorting, I want to randomly shuffle (only) the elements that have the same priority, keeping the general order of the priority.

Example:

ArrayList <myObject> objectList = new ArrayList <MyObject>();

objectList = {object1, object2, object3, object4,
             object5, object6, object7, object8, object9}

 Collections.sort(objectList)

myObject has a compareTo() method that compares the priority of two myObject.

Supose that, after the sorting, the order of the objects is:

object7
object8
object4
object5
object1 // priority = 2
object2 // priority = 2
object3 // priority = 2
object9
object8

object1, object2, and object3 all have the same priority.

How could I shuffle them without affecting the other objects?

That is, have a list:

object7
object8
object4
object5

objectx // priority = 2
objecty // priority = 2
objectz // priority = 2
// where {x, y, z} are randomly selected from {1, 2, 3}

object9
object8

I thought of doing a random assignment in the compareTo() method when it has an equality.

@Override
public int compareTo(MyObject otherObject) {
    int comparison;

    if (this.priority < otherObject.priority) {comparison = +1;}
    else if (this.priority > otherObject.priority) {comparison = -1;}

    else {
        Random generator = new Random();
        comparison = generator.nextInt( 3 ) - 1;            
    }

    return comparison;

But I suppose that when I call the Collections.sort(ArrayList<MyObjects>) the randomness will not hold.

Should I create my own sorting algorithm?

Or a shuffling algorithm?

Or does there already exists one algorithm that shuffles a specific set of elements in a list?