we already feed a stray cat- she lives in our shed and has done for the last three years. (trapped and neutered). Another stray was very kindly adopted by a MNetter's (fenneltea) mam
However a week ago a ginger and white tom sat on our doormat at the back and hasn't shifted since. He is very clean and friendly but won't go away, clawing and meowing at the back door and desperately tries to push his way in when we go out. We put a bowl of food out and he hoovered it up licking the plate around on the patio. He pats on the glass door with his paw
He's been done and doesn't spray and has a nick taken out of one of his ears
Most importantly he appears to be the first cat that dh doesn't come out with hives with or itchy, sneezing , watery eyes etc
he is currently asleep on my chair 
what can we do next?