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Question: question about saving files for supers smash bros brawl

I am new to the wii so this will be an elementary question for you...we have super smash bros for our sons ages 8 and 9, they want to play as single players and save their files separately (as they do for many other games), but my oldest son tells me they can't save two separate files on this game...is that so? They do not like to play multi-player as they end up in fist-fights! And, my older son does not want his saved information lost...any advise? Thank you!