Re: this question:
I got a great response in another forum. Here it is:
It sounds very awkward, but I can just about see it being acceptable in a very specific situation.
Firstly, I'm assuming it is NOT an unreal situation, so "would" is not necessary.
Secondly, you need to understand the difference between "like -ing" and "like to -".
Note that I'm only stating what I have read in British English grammar books.
"Like -ing" means you actually enjoy doing something, for example "I like running" (you enjoy it).
"Like to -" means you choose to do something for a reason, for example "I like to run" (to keep fit).
It's a very subtle difference and one that many would never even think about.
Usually, then, it would be more common to say "I like having a cat". However, I suppose you could probably think of a situation where you have one for a reason, for example to get rid of mice.
Thanks to everyone that helped on here. Keep up the great work.