How to implement a Map with multiple keys?

Commons-collections provides just what you are looking for: https://commons.apache.org/proper/commons-collections/apidocs/

Looks like now the commons-collections is typed.

A typed version can be found at: https://github.com/megamattron/collections-generic

This will exactly support your use case:

 MultiKeyMap<k1,k2,...,kn,v> multiMap = ??

Yet another solution is to use Google's Guava

import com.google.common.collect.Table;
import com.google.common.collect.HashBasedTable;

Table<String, String, Integer> table = HashBasedTable.create();

The usage is really simple:

String row = "a";
String column = "b";
int value = 1;

if (!table.contains(row, column)) {
    table.put(row, column, value);
}

System.out.println("value = " + table.get(row, column));

The method HashBasedTable.create() is basically doing something like this:

Table<String, String, Integer> table = Tables.newCustomTable(
        Maps.<String, Map<String, Integer>>newHashMap(),
        new Supplier<Map<String, Integer>>() {
    public Map<String, Integer> get() {
        return Maps.newHashMap();
    }
});

if you're trying to create some custom maps, you should go for the second option (as @Karatheodory suggests) otherwise you should be fine with the first one.

I'm still going suggest the 2 map solution, but with a tweest

Map<K2, K1> m2;
Map<K1, V>  m1;

This scheme lets you have an arbitrary number of key "aliases".

It also lets you update the value through any key without the maps getting out of sync.

Two maps. One Map<K1, V> and one Map<K2, V>. If you must have a single interface, write a wrapper class that implements said methods.