Is Cooper neutered? Most neutered Toms are friendly.
It is the spayed females that are problematic IMO. Sheba always kept Tippy and Oreo at length. Heaven help them if they went thru a doorway before she did! I think her behind "glands" which were always needing Vet help, bothered her and she didn't like cats close when her hiney hurt.

If he eats, uses the litterbox well, and comes out during safe times he should be okay.

At my son's house, the neutered Tom, Garfield 7 yrs is okay with the two females that were already there. Tima gets into a "thing" with him occasionally but no injuries occur. We all think it is some kind of sex game with them as it involves vocalizing. He does not do this with Ellie the tortie. At Xmas they were all in the kitchen together and they were all friendly. No stress there at all. Even shared food out of one dish. I brought them some salmon.
They don't sit together however, and each one takes up a spot
in the family room at least 4 ft away from the others.

I suppose cats can hold grudges like people, and can just dislike each other, and tolerate others. They can be very different and surprising.