In my personal experience the answer is a resounding yes. I would go as far as to say that it is essential to have a range of foods available for your cat. I have about 8 different types of commercially prepared foods and some human treats.
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I am sure the need to vary diet very much depends on the individual cat but I am convinced that the vast majority of cats like variety in their meals.
It is particularly important for indoor cats. The more variety a person can inject into their confined and therefore limited lives the better.
My cat loves prawns but he will even become bored with them if I put them down too often. The same can be said about his favourite commercially manufactured foods.
There is one food which he is less likely to become bored with: Hills Oral Care dry cat food. All high quality dry cat food appears to have an addictive quality due to the flavourings they put in it. It is artificial but highly effective in terms of taste and smell.
Why should domestic cats like a varied diet? It’s probably a throwback to their wildcat ancestor in preying upon a wide variety of animals and insects. A varied diet is in their DNA. To that you can possibly add boredom.
Well cared for domestic cats are pampered. They are hardly challenged as they would be as wildcats living in the wild. Arguably life is too easy for the domestic cat in a good home. Boredom can be a result. One way to alleviate boredom is variety in all things including diet.
Although variety should apply to small aspects of their life as cats love routine and the sameness of life too. They find reassurance in familiarity. They can become anxious quite easily I feel because they are living in the strange and unnatural world of humans, bipedal giants who are almost entirely hairless. It can be hard for them to interact.
SOME MORE ON DIET
Processed meat-based pet food is less healthy than raw food and for dogs less healthy than a vegan diet
A vegetarian cat? No. But manufactured vegetarian cat food containing all the necessary nutrients. Yes.