I have a question about battling the ancient one. Basically, I'm wondering if excess successes carry over from one turn to another. For example, if you only need one more success to remove a doom token, but you roll 3 successes. Do you then only use one success and discard the other 2 (so the success count is reset to zero), or do you take that one success, remove the doom token, and count the other 2 successes toward the next doom token? Similarly, if you are playing a two player game, you only need two successes to remove a doom token. So if you roll 4 successes at once, do you remove 2 doom tokens?

Yes they do, in both circumstances.