There are many synonyms for the phrase "remote possibilities," each offering a slightly different nuance to the meaning. One possible option is "slim chances," which suggests that something is unlikely but not impossible. Another option is "long shot," which implies that the odds of success are very low but there is still a possibility of achieving it. "Outside chance" is yet another synonym that emphasizes the low probability of something happening, while "faint hope" conveys a sense of desperation or uncertainty about the potential outcome. Ultimately, whether you use "remote possibilities" or one of its synonyms will depend on the context and the specific connotations you want to convey.