Is it possible to put more than one Pokemon in a gym?

You can be in as many as 20 gyms at once, but you cannot employ more than one of your own Pokémon at a single gym.

You can only have 1 of your own at a gym. Once it has been defeated you can take the gym back and add the same or a new one. You can add as many Pokemon to different gyms as you like but you only get the "defense bonus" from 10 gyms.

One Pokemon per gym. Unlimited gyms.

More gyms = more stardust and coins from your gym reward which you get from the shield icon in the shop.

Gyms can hold up to a certain amount of pokemon depending on their gym level. For example, a level 7 gym can hold up to 7 pokemon, however each trainer can only have one of their own pokemon on any given gym. To get more pokemon at a particular gym, you must first level up that gym to increase it's defending capacity, then wait for other people in your faction to place their pokemon at that gym.

You can have 1 pokemon in an unlimited number of gyms, but the maximum defender bonus you can collect from owning gyms is 10. For example, if I had pokemon posted at 15 different gyms, I could at most collect 100 pokecoins and 5000 stardust every 21 hours.

You can only have 1 per gym. You can have as many gyms as you want.

That being said, each gym has a base level. One Pokémon per per level. You level a gym up by training on it. It is based purely off of prestige. So if a gym is level two with 4k/8k...i believe you have to get the gym to 8k prestige before it's level 3 and another Pokémon can be placed there.

I have seen some gyms with more then one Pokemon under same trainer name. Only thing I can figure is they have more than one account with same nick name. I just found out the hard way. I took over a tower and put a weekend flareon on it so I could train and add another. I raised the gym all the way to level 4 and still couldn't add more. I really wish at the very least it would have let me take the flareon down so I could put up something stronger but it wouldn't let me so that either.

The gym mechanism has changed drastically since Pokemon Go first launched, so here is an updated answer for the new mechanics:

Is it possible to put more than one Pokemon in a gym?

In a single gym, no, you can only put one Pokemon per Gym. But, you can have up to 20 Pokemon defending different gyms.

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Some other things to keep in mind:

• Gyms only have 6 slots for Pokemon. If all the slots are taken, the button to add a Pokemon will not appear.
• You can only put Pokemon in either neutral (grey) Gyms, or gyms of your team colour i.e. Red (Team Valor), Blue (Team Mystic) or Yellow (Team Instinct).
  • You will need to battle and knock out Pokemon defending a gym of a different colour in order to return the gym to 'Neutral' status and add a Pokemon of your own.
  • Pokemon are knocked out when their Motivation (CP Heart) reaches 0. You may need to battle multiple times to knock Pokemon out of the gym.
• Gyms will only allow a single Pokemon with the same Pokedex number.
  • For example: You can't add a Charmander when there is already a Charmander defending the gym.
  • This includes alternate forms and costumes - you can't add both a Raichu and an Alolan Raichu to the Gym
  • Note that Pokemon evolutions don't share a Pokedex number, you can add your Charmander when there is a Charmeleon or Charizard on the gym.
• The Gym's 'battle order' is based on the order in which you added a Pokemon. First Pokemon added, first to battle, and potentially the first to be knocked out.
• You can earn coins for leaving Pokemon in Gyms. Pokémon accumulate one PokéCoin per 10 minutes when they're in a Gym.
  • You can earn a maximum of 50 coins per day.
  • Coins are awarded when your Pokemon is knocked out of a gym

Sources:

• Personal Experience
• imore.com - Pokémon Go Gyms: How to defend, attack, earn coins, get stardust
• Pokemon Go Wiki - Gyms