Unity system.object serialization.

Not without some extra fields which can actually store a supported serialized type. Unity serializes data based on the variable type. Since System.Object isn't a supported type it won't get serialized at all.

The best bet here would be to use the new ISerializationCallbackReceiver paired with a serialized string variable which holds the serialized data. How you serialize and deserialize your "object" is up to you as long as you can convert it into a string and be able to recreate the original value from that string you should be fine.

Here's an (untested) example to support int, float, Color and Vector3 values:

 public class Foo : MonoBehaviour, ISerializationCallbackReceiver
 {
     // our value of interest
     private object val;
     
     [SerializeField, HideInInspector]
     private string valSerialized;
     
     public void OnBeforeSerialize()
     {
         if (val == null)
         {
             valSerialized = "n";
             return;
         }
         var type = val.GetType();
         if (type == typeof(int))
             valSerialized = "i"+val.ToString();
         else if (type == typeof(float))
             valSerialized = "f"+val.ToString();
         else if (type == typeof(Color))
         {
             Color32 c = (Color)val;
             uint v = (uint)c.r + (uint)c.g<<8 + (uint)c.b<<16 + (uint)c.a<<24;
             valSerialized = "c" + v;
         }
         else if (type == typeof(Vector3))
         {
             Vector3 v = (Vector3)val;
             valSerialized = "v" + v.x + "|" +v.y + "|" + v.z;
         }
     }
     
     public void OnAfterDeserialize()
     {
         if (valSerialized.Length == 0)
             return;
         char type = valSerialized[0];
         if (type == 'n')
             val = null;
         else if (type == 'i')
             val = int.Parse(valSerialized.SubString(1));
         else if (type == 'f')
             val = float.Parse(valSerialized.SubString(1));
         else if (type == 'c')
         {
             uint v = int.Parse(valSerialized.SubString(1));
             Color c = new Color32(v & 0xFF, (v>>8) & 0xFF, (v>>16) & 0xFF,(v>>24) & 0xFF);
             val = c;
         }
         else if (type == 'v')
         {
             string[] v = valSerialized.SubString(1).Split('|');
             val = new Vector3(float.Parse(v[0]), float.Parse(v[1]), float.Parse(v[2]));
         }
     }
 }

Note: The deserialization has no checks if the string is in the required format. To actually use this you might want to implement some checks or at least enclose it in a try-catch block.