Multiple coroutines starting from Update() freeze/crash Unity

I'm having a problem with a script I'm developing.

The idea is to move a character from A(x,y) to B(x',y') in a 2D top-down grid-like map. I've done all the path calculations and the coroutine I'm using is working. The problem is, it works if I don't try to call it again before its completion. In other words and using an example: suppose I'm in A(x,y) and want to go to B(x',y'). I click the map, the calculations are made, the path is set and the coroutine starts. While the character is walking, I suddenly want to change directions and go to C(x'',y''). At this point, if I click the map again, Unity just freezes, while occupying more and more memory, and later on it crashes.

Maybe someone can help me figure this out. I've tried updating a boolean between true and false to use as a flag outside the coroutine, and also tried to call the StopCoroutine function, to no avail. If you have any idea as to why this is happening, please help.

Here's the code, by the way:

 class PlayerScript : MonoBehaviour {


 public GameObject map_go;
 public float speed;

 private Map map;
 private List<Vector3> path;

 public void Start() {
     path = new List<Vector3>();
     map = map_go.GetComponent<Map>();
     StartCoroutine(move());
 }

 public void Update() {
     Vector3 clickpoint = transform.position;
     Vector3 destination;

     bool clicked = false;
     if (Input.GetMouseButtonDown(0)) { 
         clickpoint = Camera.main.ScreenToWorldPoint(Input.mousePosition); 
         clicked = true; 
     }
     else if (Input.touchCount > 0) {
         clickpoint = Camera.main.ScreenToWorldPoint(new Vector3 
                                                   (Input.GetTouch(0).position.x, 
                                                     Input.GetTouch(0).position.y, 
                                                    transform.position.z));
         clicked = true;
     }

     if (clicked) {
         int dest_x = Mathf.RoundToInt(clickpoint.x);
         int dest_y = Mathf.RoundToInt(clickpoint.y);
         destination = new Vector3(dest_x, dest_y,transform.position.z);
         
         path = map.calculatePath(transform.position, destination);
         //StartCoroutine(move(path));
     }
 }

 IEnumerator move () {
     Vector3 dest = Vector3.zero;
     while (true) {
         while (path.Count == 0) yield return null;

         for (int i = 0; i < path.Count; i++) {
             dest = path[i];
             Vector3 src = transform.position;
             float step = (speed / (src - dest).magnitude) * Time.fixedDeltaTime;
             float t = 0;
             while (t <= 1.0f) {
                 t += step;
                 transform.position = Vector3.Lerp (src,dest,t);
                 yield return new WaitForFixedUpdate();
             }
             transform.position = dest;
         }
         path = new List<Vector3>();
     }
 }

 }

Thanks in advance!