I can implement a system where you can toggle whether or not you want to keep the same scores, but that also means that someone could just spam the leaderboard with different scores but with the same name. If you want to go with this route, then I have a solution for you that is not so straight-forward, but it involves the usage of the "Extra" field.
You could save the scores of the user locally, then every time you upload a player's score to the leaderboard, you add their previous scores to the Extra field as a string. Then every time you request the leaderboard's entries to load, you can not only display the highscores of the players, but also their previous attempts. How does that sound?