Is it possible to love someone else in the same way that you love yourself?

If you want my honest and reasoned answer then No. You can only interact someone as they relate to yourself. People and things outside of yourself will never be a fully incorporated into a part of the essential "self".
Thats not to say you can't love someone so much that they are what give your life meaning though.

I've always wondered if the opposite was possible.

Maybe that means it is.

I think that there are certain people who you can love more than you love yourself.

Your children?

Children