How to swap gameObject during EventSystem drag?

You will need to track the drag focus yourself to do this.

Replace the StandaloneInputModule component, on your EventSystem game object, with this one:

 public class DragInputModule : StandaloneInputModule
 {
     static public GameObject dragFocusObject;
 
     protected override void ProcessDrag(PointerEventData pointerEvent)
     {
         if (!pointerEvent.dragging)
             dragFocusObject = null;
         if (dragFocusObject != null)
             pointerEvent.pointerDrag = dragFocusObject;
         
         base.ProcessDrag(pointerEvent);
     }
 }

The important part to note is that the PointerEventData itself, contains the reference to the dragged object. This is how the dragged object reference is passed to the EventSystem.

Thought the only relevant line in this usage sample is:

 DragInputModule.dragFocusObject = anotherObject;

Here's the whole sample class anyway (at the 5 second mark, it switches the drag focus to "anotherObject"- it is assumed this object is an IDragHandler for the effect to be seen (I put two of these in my test scene):

 public class DragMe : MonoBehaviour, IDragHandler
 {
     public GameObject anotherObject;
     static public bool swapDone = false;
     private void Update()
     {
         if (DragInputModule.dragFocusObject == null)
             Debug.Log("currentDragObject is null");
         else
             Debug.Log(DragInputModule.dragFocusObject.name + " is the drag obect");
         
         if ((Time.realtimeSinceStartup > 5) && (swapDone==false))
         {
             swapDone = true;
             DragInputModule.dragFocusObject = anotherObject;
         }
     }
 
     public void OnDrag(PointerEventData data)
     {
         //do some actual drag move stuff
         transform.position += new Vector3(data.delta.x, data.delta.y, 0) * .01f;
     }    
 }

Please note: I've only done limited testing, but initial tests show this working.