I would enjoy having you stay with us at home

[ROBINDESBOIS]

I found this sentence somewhere. but I would say We would enjoy having you with us.
Any improvements?

[Perikles]

I found this sentence somewhere. but I would say We would enjoy having you with us.There is absolutely nothing wrong with the original sentence, which explicity has the invitation to stay in the house overnight for at least one night. Your alternative is less specific, and could mean that they would enjoy your company for an afternoon. Or ten minutes, depending on context.