[java] How to implement a Map with multiple keys?

It would seem to me that the methods you want in your question are supported directly by Map. The one(s) you'd seem to want are

put(K1 key, K2 key, V value)
put(K1 key, V value)
put(K2 key, V value)

Note that in map, get() and containsKey() etc all take Object arguments. There's nothing stopping you from using the one get() method to delegate to all the composite maps that you combine (as noted in your question and other answers). Perhaps you'd need type registration so you don't get class casting problems (if they're special + implemented naively.

A typed based registration would also allow you to retrieve the "correct" map to be used:

Map<T,V> getMapForKey(Class<T> keyClass){
  //Completely naive implementation - you actually need to 
  //iterate through the keys of the maps, and see if the keyClass argument
  //is a sub-class of the defined map type.  And then ordering matters with 
  //classes that implement multiple interfaces...
  Map<T,V> specificTypeMap = (Map<T,V) maps.get(keyClass);
  if (specificTypeMap == null){
     throw new IllegalArgumentException("There is no map keyed by class" + keyClass);
  }
  return maps.get(keyClass);
}

V put(Object key, V value) {
  //This bit requires generic suppression magic - but 
  //nothing leaves this class and you're testing it right? 
  //(You can assert that it *is* type-safe)
  Map map = getMapForKey(key.getClass());
  map.put(object, key);
}

void put(Object[] keys, V value) { //Or put(V value, Object ... keys)
   //Might want to catch exceptions for unsupported keys and log instead?
   .....
}

Just some ideas...