I belong to a few online, social media photography groups, mostly headshot oriented. It's interesting to see the numerous set ups and variety of gear used by a lot of headshot photographers just starting out. I see people wanting to pull off one particular style of headshot but going way overboard with their attempts. Then, inevitably, they struggle with why they're not nailing their shots and or....their work is not consistent. Why? Simply because they're over thinking it sometimes and getting too caught up in trying to get fancy with their work. Now obviously, there's no one size fits all set up or formula for every photographer but, I should think that within the realm of shooting headshots, even with different styles of lighting, the overall look isn't going to vary too much.
Shooting fashion for example can involve one light or twenty lights, a plethora of modifiers, tons of gels, reflectors and flagged off sections of studio or location space. The actual job itself and/or the photographer's vision/client's vision dictates the lighting and overall look. There's a heck of a lot more room for creativity and you're not always shooting the same thing. Not to mention the post processing, color grading and all sorts of stuff used to create the final images. That said, if you're shooting fashion on the regular, chances are you've got a variety of gear that's used based on need and what look you're going for.
With a headshot on the other hand, you're shooting one thing - A tight shot of someone's face/head. It's a shot to represent the person and their personality and to get an actor work. While there are different opinions on landscape vs portrait and studio vs location, either way you're pretty much going to have a basic set up each time and it's not about clothing or shoes or jewelry, hair or styling. It's about that one person in front of your camera. Give or take a few personal preferences, it's a pretty basic set up - Your key light to light the subject, some fill and possibly some type of kicker/accent light. That should really be it for the most part. (In studio, if doing the high key, white background thing, you'll have lights to light the background.) The type of lights you're using, which modifiers and how you set it all up is of course, up to you. Even if you're strictly a natural light headshot photographer, you've got one consistent source of light (the sun) and chances are you'll have some sort of fill via a reflector. All of that said, the main thing I want to get at in this post is that you truly need a consistent, go to set up for your work when shooting headshots. There really shouldn't be the same experimental, freestyle, artistic license thing going on as there may be for fashion, editorial or a random portrait.
While you can always play around and have 6 to 10 lights , 3 oversized, octagon shaped reflectors and miscellaneous contraptions and set ups to light one person for a headshot, it may not be the best idea and probably overkill. You should keep it simple and not go overboard with trying to do anything fancy other than lighting your subject the best possible way. You need to consider what style of headshot you want to shoot, learn how to do it, what you need and then...stick with THAT set up on a regular basis. THIS is how you nail consistency. And consistency is what ultimately will serve to make your brand. You can always make a few adjustments/changes here and there and possibly experiment once in awhile, there's nothing wrong with that. But, you should commit to your main set up, know your gear, master that set up and repeat it over and over and over!