operator[]= overload?

You can overload operator[] to return an object on which you can use operator[] again to get a result.

class ArrayOfArrays {
public:
    ArrayOfArrays() {
        _arrayofarrays = new int*[10];
        for(int i = 0; i < 10; ++i)
            _arrayofarrays[i] = new int[10];
    }

    class Proxy {
    public:
        Proxy(int* _array) : _array(_array) { }

        int operator[](int index) {
            return _array[index];
        }
    private:
        int* _array;
    };

    Proxy operator[](int index) {
        return Proxy(_arrayofarrays[index]);
    }

private:
    int** _arrayofarrays;
};

Then you can use it like:

ArrayOfArrays aoa;
aoa[3][5];

This is just a simple example, you'd want to add a bunch of bounds checking and stuff, but you get the idea.

It is possible if you return some kind of proxy class in first [] call. However, there is other option: you can overload operator() that can accept any number of arguments (function(3,3)).

For a two dimensional array, specifically, you might get away with a single operator[] overload that returns a pointer to the first element of each row.

Then you can use the built-in indexing operator to access each element within the row.

An expression x[y][z] requires that x[y] evaluates to an object d that supports d[z].

This means that x[y] should be an object with an operator[] that evaluates to a "proxy object" that also supports an operator[].

This is the only way to chain them.

Alternatively, overload operator() to take multiple arguments, such that you might invoke myObject(x,y).