I think I'd say It's not only you who likes to invite people to their/your house, but also me. Now, both "their" and "your" have some problems. With "there" , it's almost as if you're inviting people to their own houses.
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demion"It is not only you who likes to invite people in their house, but also me." Is this sentence correct?It's OK except that 'in' should be 'to' or 'into'.
demionHow much can I rely on your "I believe" and "it's unlikely"? Do you have an idea how can i express the same thing more accurately?People use common sense when they communicate, so unless your sentence is said in a very unusal context, the chances of your being misunderstood are practically non-existent.