Totally agree with Rick, Dye. Two (or more!) cockerels in the same pen will fight, causing injuries and possibly the death of one of them. Also, even only one cockerel will wear away the feathers on the backs and sides of his favourite hens, possibly even causing scratches and injuries - that's why some people make their hens wear hen saddles to limit the damage. So, in trying to improve feather growth on bald patches, you would only be making a different problem of feather loss. As Rick says, adding any more birds is going to increase stress in the flock, and in any case, with your 15 hens all now adult and settled into their pecking order, a new cockerel would have his work cut out to manage them all, and might well end up being bullied himself. The proper way is to set up the cockerel in a separate run and then introduce the hens one at a time. Just putting any single bird into an established flock is a recipe for disaster. More birds also means more mess, and in your case, more rats.
Don't do this. I don't know who your friend was that dished out this advice, but its clear to me that he's not a very experienced poultry keeper! To say that the hens are pecking each other because they're horny, in the middle of winter and out of the breeding season, is complete rubbish.