Eternal Happiness is very similar. Well, it has nearly the same synopsis, but it develops in its own unique way. It didn't give me as much laughs as MBP, but it is a good story.
You might enjoy
Love at First Fight also. It is not a well know series, but it was funny.
Another romantic historical gender-bender (just like the above) is
Sungkyunkwan Scandal. It has a lot of funny moments, but I think it has a more complex story. This is one of my all time favourites.
A modern, but still cute gender-bender is
Coffee Prince. Also
Hana Kimi is well known.
There are more gender-benders of course, but start with these.
Then.. outside of the Asian drama's... hmmm... well of course you have
Twelfth Night or What You Will. Very funny, but the gender changing isn't because of saving other people. A modern adaptation of this film is
She's the man.
If you enjoy anime, you might like
Ouran Koukou Host Club (also has a Japanese real-life adaptation). But here it is also not a gender-change because the girl wants to save people. Another funny series is
Tenshi na Konamaiki.
Hope you find something you like. If you want more titles for the gender-bender genre, let me know.