Is there an idiom that means something like that? I am especially looking for an idiom that says "you should keep trying different things", but not "just persevere", I am especially looking for the idea of "different things being tried". Otherwise, I would have asked for an idiom with the theme of perseverance.
Yes, there is:
If at first you don't succeed, Try, try, try again.
That is a well-known saying.
Hickson is credited with popularizing the proverb:
'Tis a lesson you should heed: Try, try, try again. If at first you don't succeed, Try, try, try again. The proverb can be traced back to the writings of Thomas H. Palmer in his Teacher's Manual, and The Children of the New Forest by Frederick Marryat.
You will hear people throw out a quote that's been attributed to Albert Einstein, Mark Twain and Ben Franklin, but probably didn't come from any of them.
The definition of insanity is to do the same thing over and over and expecting different results.
This idea is used in all different situations. It's not exactly an idiom, but it is very commonly expressed to illustrate the idea that if something is not working the approach needs to be changed.
I don't think there's any other suitable common phrase or idiom.