How to define []= and at() = for a custom collection?

There is no []= operator. If your operator[] function returns a reference that can be assigned to, that's all you need.

Simple example to demonstrate the idea.

struct Foo
{
    int i;
    int& operator[](int) { return i; };
    int operator[](int) const { return i; };
}

Now you can use

Foo f;
f[10] = 20;   // The index is not used by Foo::operator[]
              // This is just to demonstrate the syntax.

You need to do the same with the at() function.