You can use "beyond" (in the sense of "more than" or "even more than") with a variety of adjectives or descriptive nouns, but generally speaking for an adjective I think that that will only feel natural if the adjective already represents an extreme description. For example:
* he was beyond terrified
* he was beyond desperate
* his performance was beyond hilarious
* his feelings for her were beyond adoration
* he was beyond amazement/amazed at her performance
* his reaction was beyond indignation/indignant
Adjectives such as funny, intelligent or widely-read (your examples of positive adjectives), or upset, annoyed or disappointed, might be too tame for "beyond" to feel nature. That might be different with a noun, e.g.:
* his emotional reaction was beyond disappointment
* their response was beyond silliness
I guess the reason for pairing "beyond" with adjectives or descriptive nouns that have a superlative or extreme meaning is that "beyond" is being used to mean "even more than", which is comparing A to B on the basis that B is already fairly extreme, and A is even more so. Consider how I could sound naturally telling you that a beer costs $20 (USD) in one particular bar and even more in some other bar, but that would sound silly if I had said $1.