The factory with two 'build' methods

In my application I have many types of entities - they have one common interface let say

public interface MyEntity {
    String getCode();
}

Entites are being sent from fronted wrapped in some kind of request like

public interface MyRequest {
    MyEntity getMyEntity();
    String getOperationType(); // this can be one of 'CREATE', 'DELETE', 'UPDATE'
}

After performing my business logic, based on request's operation type and the entity that it includes, I need to run some post-process operation and this operation is custom for every pair of 'operation-entity' - for this I created a factory like

public class MyFactory {
    private Map<MyKey<String, String>, MyOperation> postProcessors;

    public MyOperation getOperationFor(String operation, String entityCode) {
        ...
    }

    public void addOperation(String operation, String entityCode, MyOperation operation) {
        ...
    }
}

The problem is that I need to perform some additional postProcessing after every Operation, base on it's type, no matter what entity code I've received - e.g. "after every creation send notification to x@y.com" etc

My question is how to resolve this? I feel that adding to the factory additional Map<String, MyOperation> and add/get methods for this is not a good idea - should I create additional factory? Or maybe I should create add/get methods but keep MyOperation objects for operations with null in the place of entityCode?