As long as the birds have plenty of room to roam, roost, nest and plenty of fresh clean water and do not need to fight for food and you keep the range clean of fecal debris (raking and removing manure on a regular basis), you can keep multi-species birds together with great success.
Always take into consideration that each species does carry it's own different micro-organisms in the fecal content and that you will need to keep a close eye on them, especially while they are young, to prevent any cross contamination.
Example: Turkey's carry micro-organisims that chickens are not immune to, and ducks carry M.O that other birds are not immune to etc..
We have grown multi-species together for over 20 years with great success (not swans), that being said, we are in a dry region, and we feed Certified Organic feeds, and do not vaccinate. Sometimes vaccinated birds can get very ill and cause cross-contamination within the flock, which can cause viral and/or bacterial mutation.
In an effort to minimize and prevent intestinal fungus and fecal cross contamination, we do not use any G.M.O's, no corn, no soy, no wheat and we develop our own feeds to compliment the free-ranging and foraging of all our flocks.