Definitely agree re feeding a 'secret cat'.  That's usually how you end up with another feline who is very quickly no longer a secret!

 

A co-worker already had a cat when another suddenly turned up in his yard.  No one claimed him despite neighbourhood enquiries, so food was left out.  I told him he had just acquired a second cat.  He said he hadn't.  I said he had because being a cat fan, there was no way he could suddenly stop feeding the stray and shoo it away.  He thought about it for a minute...and agreed.

 

He now has two cats, the stray having been checked over by a vet (no microchip), desexed, de-fleaed etc.  His original cat was initially not very impressed, but as time goes by they are gradually becoming used to each other and there's been no fighting.  Definitely a win-win situation for all.