Interesting thread. Can't account for how they do it at other airports. (Yeah, I know, I am including this in most of my comments. That's because the responses I get are, "well, at airport xyz they made me....blah blah blah.")

Coats, sports coats, suit coats, blazers, jackets and athletic running jackets have to come off. That's the rule. However, there is room for common sense. If I see a woman wearing what appears to be a suit coat, but I cannot see anything indicating a blouse underneath, and what I'm talking about here is seeing nothing but skin where the coat is buttoned and forms a v-shape, I will ask her if she minds removing her coat. If she tells me that she does mind or says that she doesn't have anything else underneath that is presentable in public, I will then have her come through the walk-thru still wearing the coat. At this point, I have to make a determination if the material is thick enough to conceal any non-metallic prohibited item or weapon or if there are any unnatural bulges (shapes inconsistent with the natural contour of the body) before I decide to refer her to secondary screening or allow her to pass if she doesn't alarm the WTMD. Sorry, ladies, but leather coats will automatically get you referred to secondary screening.

If I see a loose-fitting garment that is unbuttoned, unzipped, unsnapped, and the woman is clearly wearing something else underneath which may be a t-shirt, tank top or camisol, I will ask her if she is wearing a jacket. If she says she is, I will ask her if she minds removing it. If she says it's a blouse, I will let her pass through. If it is made of thick material, I will make a determination if it's feasible that something else could be concealed underneath. In most cases, the material sways open enough that I feel reasonably confident that there is nothing else concealed underneath. If I have any doubts, then I refer the lady to secondary screening.

I've only addressed how I handle female passengers in this post because it's usually not an issue with male passengers, although I have had some men complain to me when asked to remove a jacket.

One last thing, and I've posted this before so bear with me if you've read this before. Some women are completely uninhibited and, I believe, look for opportunities to show off. I remember a lady who was wearing a western style snap-button shirt over her tank top that was partially buttoned with the bottom of the shirt tied above her waist in a Daisy Duke fashion. She asked me if she should remove her shirt because of all the metal buttons. I told her I didn't think it was necessary and thought she was going to come in. She hesitated and said she really didn't want to undergo secondary screening if she alarmed the WTMD (this was before we implemented the double-pass policy). I told her that usually things like large belt buckles or watch bands would alarm the WTMD but buttons on a shirt wouldn't. She unsnapped her shirt and threw it in a bin and walked through with her tank top revealing her artificially enhanced features. I then overheard her say to the passenger in front of her, "they always make me take off my shirt." To add insult to injury, the female screeners eyed me suspiciously as the lady obviously drew the attention of everybody at the checkpoint.