Because you love them individually, they will work when you use them together and achieve an inviting and comfortable feel to your room.
The more themes you incorporate, the more creative you will have to be but the process is basically the same. It will also depend how similar or different the themes are. Combining some themes like an Asian theme and Zen theme would be easier than a Zen theme with a rock-star theme. The primary task here is to identify the common factor in the living room ideas. For instance, in combing an Asian and Zen theme, you would incorporate a more natural Asian representation like bamboo, jade and the concept of feng shui. You could also incorporate meditation cushions that would be used in Zen lifestyle and simultaneously represents a classic Asian seating arrangement.
Having said that if you do have the money to purchase some new furniture then that is a lot more fun. It is important to set a budget though prior to looking as you know what it is like when you are out shopping and you get carried away with what you see.
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