Do you think it is possible, in a novel, to use multiple first person perspectives (each perspective having a set of scenes) in which there is no obvious distinguishing mark other than voice? For example, Scene 1 is from one character's perspective. We know that scene 2 is from another character's first person perspective because the voice has changed. We know that scene 3 is from the first character's perspective because the voice is the same as Scene 1. I'm toying with this idea, but I don't know if it would work.
Write it, only make your prose a joy to read, rather than some headache where I'm tootling down the page thinking 'why the hell is he wearing a bra,' etcetera.
Yes, there are plenty of examples out there of multiple POVs that work. You need to be careful how you do it, though, and I don't get it why you aren't identifying the characters. Even if you have a twist like multiple personalities in one person, generally at least one of them should be talking about the other so the readers knows they are two different personalities. Or there may be another way to indicate it, but just voice alone sounds to me like you will be missing a large piece of these characters by not describing them more fully.
Presumably the reader would have to read some way into each section before working out who the main character is. During this time, the reader won't know what's going on and may become confused if he/she makes the wrong guess. It's easy for an author to perceive a great deal more in the text than a reader may pick up. I would say that you need to make it abundantly clear to the reader what's going on for this to stand a chance of working. Above all: Don't confuse the reader.
Trainspotting by Irvine Welsh immediately springs to mind. You have to make sure that each character has certain identifiable nuances and certain specifics in their narrative that allows the reader to make the connection to the character. It can be done.
This is one of those things that can be done—and possibly to great purpose—but very carefully. I love @matwoolf 's comment. He's pretty much nailed on the head what can go wrong! I'd say go for it, but test it out on several beta readers ...without telling them what you're doing. Listen very carefully to their feedback, and see if you can address any concerns they might have.
Honestly, I often have a feeling about something before I know why. It used to happen a lot when I worked in computer security. My gut feeling pushed me in a direction and, as I followed it, I'd collect data which vindicated my gut feeling. I'd get the system up and running while my colleagues were back at square one and I might or might not have been able to explain why. Has that ever happened to you? There's just something in my gut which is telling me to go in this direction. But, I'm not as experienced an author as I was a computer guy. So, I'm looking for a reality check.
I suspect there are a few ways to do this well, and a great many ways to do it badly. As well as the question 'would this work?' ask, 'is this best?'. I'd write a few sections in multiple first person as suggested, and re-write the sections in third person. Then ask beta readers which they prefer.
It works.....nuff said. Well, when it's done competently, at any rate. It also adds something of value to the novel. I have to say, I do enjoy this when it's done. It gives you that different perspective to events (one way of identifying that particular character) and takes away any boredom. You know, to start a new chapter and think, 'oh great, it's MC3 speaking, I love hearing his sarcastic opinions'....that makes reading a joy, bra or no bra.
It's tricky but doable. What I'd do is to have the character name be underneath 'Chapter' header, or have their name be the chapter header entirely. Also, I'd love to read a POV where a male character is wearing a bra, high heels and make up.
Sue Grafton's T is for Trespass comes close. She refrains from switching perspectives other than on chapter boundaries. If I recall, the chapter heading indicate the switch, but Grafton's use of voice is clear enough that you would not be confused even if there were no cues in the chapter headings. It's risky though. Not all readers pay close attention, and if they get lost, it doesn't really matter whose fault it is.