Can you raise free-range pigs, sheep, goats and chickens all together?

No not really. What many do is rotational grazing where they run different animals one after another in the same pasture. So start with cows, than when they move to their next pasture (and when you pasture/free range livestock you have to have many pastures/paddocks to move them onto once they start to eat town the forage so the forage can grow back). than put the chickens and they will break up the manure as well as eat parasite eggs that afflict the cattle (but don't do anything to the poultry), than run the sheep than run the pigs. Joel Salatin has written many articles and books about this kind of rotational grazing When doing this sort of thing chicken are kept in movable coops called chicken tractors

Very interesting question. No problem if your pasture is big enough to sustain these animals and birds. They will form their groups and separate themselves from other kind. Animals and birds like human are different nature; some are peace loving others are quarrelsome. You have to pay close attention and segregate the bullies. Some individuals develop liking for some other kind some hate individual animals; see to it this hatred doesn't cross limits. As far as enclosures are concerned it is better to separate kinds by putting a wall in between sections. Bullies should go in to individual section. Good luck.

here is a link called The Concerns With Keeping Different Types of Livestock Together http://factoidz.com/concerns-with-keeping-different-types-of-livestock-together/ I personally keep sheep- and free range hens - also a llama, and donkey.

YES.............& your losses would be UNACCEPTABLE.