Giving Scriptable Objects a reference to a custom abstract class - unity3d

Question

I'm working on a 2d Topdown game for my senior project, and I'm coming across a bit of a design issue. Currently, the plan is for the player to be able to hold 1 weapon for each of three classes (melee, ranged, magic). They can pick these items up on the map, and it will be added to their inventory. These items carry 2 attacks each, and whichever weapon is active in their inventory gives the player their two attacks they can use.
Here's the base class for the Item ScriptableObject:
public class BaseItemSO : ScriptableObject
{
[SerializeField] private string itemName;
[SerializeField] private string description;
[SerializeField] GameObject model;
[SerializeField] Sprite inventoryIcon;
public string getName() { return itemName; }
public string getDescription() { return description; }
public GameObject getModel() { return model; }
public Sprite getIcon() { return inventoryIcon; }
}
The GameModel holds the item's overworld sprite, its collider, the usual stuff.
Then we have the WeaponItemSO. This inherits from Item, and it meant for the weapons that the player can pick up. It has a weapon class (same melee, ranged, magic) and I'm attempting to give it two references to some sort of Attack script.
{
[SerializeField] private WeaponClass weaponClass;
[SerializeField] private BaseAttackController attack1;
[SerializeField] private BaseAttackController attack2;
public enum WeaponClass
{
Melee,
Ranged,
Magic
}
}
The problem I'm running into is that each attack has a different script. I haven't implemented baseAttackController, but the plan was for each to have an OnAttack() and dealDamage() and whatever else is necessary, and these attacks could be read from the WeaponSO that the player holds. Unfortunately, Unity can't serialize these abstract classes or interfaces. What might be a pattern I should go about here?
I haven't implemented further yet, but my ideas have included simply putting those attack controllers on the GameModel that is referenced. Then the player could read that, but it certainly doesn't feel like the right approach, the attack class should be able to exist with or without a player or gameobject.