It's all up to you.
The answer is yes.Only if you have the time and patience to clean,care,shelter and water them all correctly if you said,"no I can't,"well then don't try it.It also comes with risks.
1.the protozoa Histomonas meleagridis lives in most poultry environments except where the soil is dry,loose and sandy which is also known as Blackhead it is a devastating disease which can kill all your turkeys this can happen when chickens and turkeys are together but a lot of people keep both species together never encounter such a disease(like me)
2.chickens like to roost ducks(except tree perching ducks such as muscovies,wood ducks,etc.)and geese don't so they will likely try to sleep underneath perches to feel close to their other friends what do chickens do? They poop. The unlucky duckies can get sick from such a unsanitary situation.
3.turkeys also like to roost but a chickens perch has to have the diameter right for their feet same for turkey's otherwise you could encounter foot problems
4.ducks and geese love water and will make a muddy mess unless handled that is if you allow them swimming water(please don't keep ducks and geese unless you allow them water for swimming they love it and what's a duck or goose without water?)and if you do chickens and turkey's will drink out of their mud puddles which can lead too Infectious Bronchitis which is a type of respiratory disease(ducks and geese can get this as well but they seem to have a higher tolerance for such a disease)
5.mud from your water fowl can also lead to bumble foot which all four species can get it starts from a small infection of the foot to a large abscess which not treated causes severe pain and paralysis in the affected legs
6.also can you provide a large enough shelter for such a flock?
Prevention from such risks:
1.keep a clean coop to the best you can manage and probiotics/vaccinations when young will also strengthen the immune system and probiotics around the home would be yogurt,apple cider about a teaspoon per liter and a weak poult could do well with some table sugar in their water same dosage
2.don't allow for your ducks and geese to sleep underneath perches as simple as that
3.have separate perching spots for each specie they can still be in the same coop just different spots with the right-sized perches for each specie
4.gravel your coop or just the water area would be the best alternative
5.same as 4.and don't leave sharp objects lying around that they could cut their foot on
6.this depends on your budget
All these simple prevention can mean life or death to the whole flock.
1.I always recommend rubber before the large mental troughs after a couple years their rusty garbage with holes I use a trough like this for my geese and ducks to swim in
2.I use several of these as food dishes easy to clean and don't rust and aren't too light and I would provide several feeding areas so the lower ranking members get to eat too
3.These are nice perches for chickens(this is not my picture and thanks to whoever it might belong too)
My flock saying hi these are my pictures!
Sorry about the light.
If you would like more information on the care of your flock feel free to pm me or join my chat thread!