Problem with unity grid step movement

I am having problems with my player movement script. At the moment I am checking in the update method if the button has been pressed and then running this coroutine. The problem is if I press the button twice fast the player records the position between the positions and moves outside of grid, if I limit the movement with "canMove" for the duration of coroutine I have to wait for the player to reach the destination before giving another moving isntructions with makes the game a lot less dynamic. How would I go about making it so that the player can receive couple of movement instructions in advance. For example if I press right and right again while moving he would finish the first movement and then move again the same amount a fixed step over time.

Here's the script:

 IEnumerator MoveFast(Transform objectToMove, Vector3 targetPosition, float jumpTime)
  {
         canMove = false;
         float t = 0;
         Vector3 originalPosition = objectToMove.position;
 
         while (t < 1)
         {
             t += Time.deltaTime / jumpTime;
             objectToMove.position = Vector3.Lerp(originalPosition, targetPosition, t);
             yield return null;
         }  
         canMove = true;
     }
 

And in the update:

  void Update()
     {
         if (canMove)
             KeyboardMovement();
     }
 
     void KeyboardMovement() {
         if (Input.GetKeyDown(KeyCode.DownArrow))
             {     
                     coroutine = MoveTo(transform.position, transform.position +
                     new Vector3(0, -4, 0), 0.5f);
                     StartCoroutine(coroutine);
             
             }
     }