Yes and no! ^^

• Yes, you can create your own event type taking a parameter and assign dynamic callbacks to it. What you are looking for is UnityEvent.

  For the dynamic parameterized ones see UnityEvent<T0> to UnityEvent<T0, T1, T2, T3> depending on how many parameters you need.

  For the example with a single int it would be (exactly as in the API example)

  // Since Unity doesn't support direct serialization of generics you have to implement this [Serializable] wrapper
  [Serializable]
  public class MyIntEvent : UnityEvent<int>
  {
  }
  
  public class ExampleClass : MonoBehaviour
  {
      public MyIntEvent m_MyEvent;
  }
  

  

• No, you can not simply change the existing implementation of UI.Button.onClick which is parameterless.

  What you could do, however, is build a new component and attach it on a button like

  [RequireComponent(typeof(Button))]
  public class ExampleClass : MonoBehaviour
  {
      [SerializeField] private Button _button;
      public MyIntEvent onClickWithIntParameter;
  
      private void Awake()
      {
          if(!_button) _button = GetComponent<Button>();
          _button.onClick.AddListener(HandleOnClick);
      }
  
      private void HandleOnClick()
      {
          // Wherever you get your int from
          var value = 123;
  
          onClickWithIntParameter.Invoke(value);
      }
  }