It's generally considered good style to use the same preposition when making lists of things, but it's not a grammar rule. For example:
Tomorrow we plan to go to the museum, to the library, and to the shopping district.
Of course it's possible to mix up different prepositions, but then it's not really a "list" of similar things.
Tomorrow we plan to go to the museum, on the train, with our friends.
It may be helpful to memorize English verbs as verb-preposition pairs, since the meaning can change depending on which preposition is used. For this reason it's difficult to think of an example where you can mix prepositions but still have all of the objects relate to the verb in the same way.
For example, in the above sentence what other preposition would you use other than "to"? "Resort to" is (more or less) the only verb-preposition pair that works.