Room or flat with pets accepted

I’m looking for a room or a ground-floor flat and I have three very calm, cats. They are peaceful, well-behaved, and mostly sleep during the day — they’re really low-maintenance.

I’m happy to pay a bit more than the standard rent to help cover any concerns. I would really prefer not to have to give them up if possible, as they’re part of the family. I’ve been finding it difficult to find a landlord who’s comfortable with pets, so I truly appreciate anyone willing to consider this. My currently landlord is very happy with the being around and would give a reference.