I can't remember whether you've ever seen me working, but I tend to use lights much closer than most, which means that I don't need a great deal of space - but because I'm lazy and also tend to work fast, I like to have loads of lights, fitted with a wide range of modifiers, these tend to just get pushed to one side when not immediately required, taking up space but facilitating fast work. When I've had to shoot in a small space I've got around this by putting things away, but this dramatically reduces speed.
I'm definitely of the Garry Edwards school of studio craft - no matter how long a shoot is, I always have more to do than I can get done (although partly, this is deliberate - imagine running out of ideas half way through a day's shooting?), and will use any dead time (make-up, wardrobe, model's cigarette/coffee/phone break) to queue up lights, and other gear for the next shot and the one after that. I also shoot mostly in small studios though and I'm terrible at the "putting stuff away" part. If it's not raining, I'll sometimes sling stuff outside after it's done with, but mainly, the studio looks like an explosion at WEX by the time I've finished. I then need to track down and recover all the gear I've strewn about the place. Usually it's nearby, but I did shoot at Joel Hick's location (his dad runs an industrial estate, machine shop and museum which they also rent out for shoots), and we had to drive around picking up lights, stands, other misc grip gear, smoke machines etc. afterwards from machine shops, warehouses, on top of JCB's...
I tend to order my set plan, grouped on the things that are most time consuming to change, ie: makeup and hair, followed by background (it's not just the act of swapping the roll in a small space - you need to move all of the lights and other gear off the background to change it). The one thing I do need to fi though is I tend to over-shoot stuff - ie I'll make too many minor variations, which later, when I sorting through the images, just don't make any difference - too many of therm are the same.
I used to worry about shooting in small spaces, and look for studios with more space, and sure, you can do things in a larger space that you can't do in the small one, mainly, shoot from further away, which gives a different look to the images, or shoot closer and wider without running out of background. On of the ways I solve this these day is to shoot for post production. That is, I'm not "fixing" the image in post, so much as adopting a an end-to end workflow where the capture part is just one part of of the whole process. One of the things I do in small spaces is to maximise the pixel coverage of the subject - so I shoot vertically. The final image though will often be a 16:9 widescreen at ~120MP. Photoshop is just so good at making up excess background these days: I used to do this once in a while as cretaio of the extra space was a laborious process of cloning, flipping, stretching, warping etc. Now, with content-aware crop, you can add extra background pretty easily. Not in one go, but you add a bit at a time (say 15%) and then clone and disrupt any patterns that start to form and then do a bit more. Once you get pas 1:1 I'm just try a 16:9 in one go and usually go from there -takes about 10 minutes now.
Other than that, it is, as Garry says, about light control - closer lights, barn doors, flags (I'm favouring black foam core on bendy grip arms right now) grids and black walls, black floors and cloths. To solve that "large softbox won't fit under the low ceiling" problem, just aim a light up at the ceiling instead and let that be your soft light source. Just be sure that none of the light goes directly to your subject - so again grids, barn doors etc will help Or a Large BFT
F2 ran a feature on shooting in small studios once, and they called Garry asking for some potential interviewees. Garry was kind enough to suggest me, and here's the article they wrote on me which starts off "Owen Lloyd is interesting..." which is all I ever wanted
I've moved house since then and the current studio is a little big bigger than the attic room you can see here, but it's still pretty small. I'll grab some picture of it later on and post them up. One of the things I would also urge you to do, is consider the whole contiguous space - not just the room you've designated as the studio space. For example, in my current setup, the studio door opens onto a 2nd floor landing off to the eft of the "shooting wall", so I can put a light out there for example, if I want it further away, or shoot from out there along the background wall. The room also has double doors opening onto a very strange balcony affair, which is next to useless tbh, but it does add an extra metre of room if It's not raining... (I've also boomed lights out from there pointing back into rooms below
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Also - check out Barry Mountford: his DIY overhead lighting track is brilliant.
View: https://www.youtube.com/watch?v=79TX_OHJ8KQ