Can indexers be redefined in a Dictionary-inherited class?

I am trying to implement a MultiDictionary: a Dictionary which holds a List in each key.

I want to be able to add elements to the dictionary using the addition assignment operator and indexers :

myMultiDictionary[key] += elementToAdd;

I first created a custom AddableList which inherits from List and overloads the + and - operators, which let's me use the addition assignment operator :

myAddableList += elementToAdd;

MultiDictionary is then a simple inheritance of Dictionary<keyType, AddableList<contentType>>.

I'm having problems with the indexers. I wish to keep the Dictionary inheritance to use the O(1) performance of dictionary keys. However, I have to redefine the indexers to:

• create an empty list if I create a new key;
• delete a key if I remove all elements in the list.

How does inheritance work for classes where indexers are already defined? Will my new indexers overwrite all access methods defined in dictionary?