Quote Originally Posted by Throbert McGee View Post
If you were speaking in the singular familiar to a girl/woman, would the construction be "Сегодня ты превзошла саму себя." ????

I'm trying to clarify that the verb is followed by the accusative, not the genitive (which would be самой себя in the feminine singular).
Indeed, ты
превзошёл сам себя
превзошла саму себя
превзошло само себя (if one can imagine referring to neuter gender interlocutor: "свет мой, зеркальце, скажи" and all this stuff)