Can there be more tha one relationship (SYNONYMS, HOLONYM, etc) between two words in WordNet? Logically, I would say no but with different senses, is it possible?
You wouldn't get that from WordNet. You need context for that purpose and there is no context in WordNet. You can try Roget's which has some sort of conceptual taxonomy of words [starting from abstract concepts and becoming more specific], but in terms of coverage it's no where near WordNet. Perhaps you would require to look into ESA which provides a similarity metric based on Wikipedia. Also, have a look at the popular word2vec.