I looked at building a rat-proof potato bin that allows them to breathe - I've got all the materials so should be done later in the week. Rat traps reset and positioned in the potato store may catch one but rats ain't stupid..
Still could be worse.. Rat in Mi Kitchen
I had occasional problems with rats in the kitchen ceiling & under the floor throughout the house.
Whilst poison got rid of them, irretrievable carcases were a tad smelly for a week or two..
Mid 19th century sandstone terrace & I couldn't find how they were getting in.
Then my neighbour had his adjoining kitchen extension roof replaced & the problem went away...

On cats: Had them for 45 years, mostly 2-3 at a time, one young, one middle aged & one older. So long as the youngest is introduced as a kitten, even the oldest has always accepted their presence, often enthusiastically. Never had more than one Tom at a time though & Queens are always better hunters.