it is possible, but sometimes the females of the other species will sort out the dominance heirachy between themselves and one will emerge a male from the females. at the end of the day, you will end up with male of fairy species a), and a male of fairy species along with remaining females of the latter. unless of course the male of a) is so aggressive that under such intense pressure, females will never get a chance to morph.
male fairy wrasses can hold their color for many reasons. here are some possible scenarios.
1) by constantly displaying to other males of another species, the dominant male will display beautiful coloration. some cases the less dominant male of another species will get less colorful as it is being dominated, or sometimes the other species will exhibit heightened color as well as two species constantly pit themselves against each other.
2) by keeping the male with multiple females of the same species. this is the best way IME, and the males will regularly spawn with gravid females.
3) some species can hold colour very well even if kept alone with no other species or females, while others can never hold coloration even with females. one example of the latter is C. scottorum, while the former applies to C. jordani or C. earlei.
at the end of the day, it really boils down to the individual fish's temperament, the specific species, and its tank mates. some species will never hold coloration unless kept in a peaceful tank and it is the only species allowed to dominate, and kept with females. shy species such as C. marjorie for example. other more boisterous species can be kept with multiple other fairy wrasses of different similar genders without females and will thrive under competition, such as C. laboutei.
the best way to keep Cirrhilabrus and paracheilinus is to choose 1 or 2 species you really like, get a male and 1-2 females. this is the best way to enjoy the genus. mixing too many species together will result in messy and heightened aggression between species and will often result in one or more losing coloration or hiding.