I've done this with gum and casein prints many times. With standard color paper (RA4), it wouldn't be worth the headache, as the registration would be a nightmare.
I'd recommend also shooting one negative without any filter. If you want, you can underexpose it or under develop it. The reason being, you'll get a lot more dynamic of a print if you also have a black layer, but you don't want 100% black. Usually something like 20-30% is all you really need to fill in the shadows and add more depth. You can also develop the unfiltered negative like normal, and just back off the pigment or exposure during your print stage.
Basically, up until the 90's, this is how all print shops printed CMYK, four color process magazine, brochures, pamphlets, books, etc. You made a life sized mockup of whatever you wanted to print, taped it to the wall, took an extremely large (like the size of a room), large format camera, and took four negatives of the image, using the red, green, blue, and no filter, to make your cyan, magenta, yellow, and key (black) plates. Then the negatives (which would be huge, by the way) would be used to expose your plates which would then go on the press to print whatever it was you were printing. Or sometimes the negatives would be the plates themselves, depending on the chemistry involved. It's a fairly simple process, though messy, expensive, and time consuming. Which is why it's all done digitally these days. Now they use a what's basically an industrial CD burner to burn the image onto a pre sensitized plate. No chemicals involved. They've even got large digital presses that bypass the need for plates all together, and just act like industrial sized, super high speed inkjet printers.
As a bonus, you don't have to use red, green, and blue. You could use any color filter and then print it with it's complimentary color pigment. Though RGB tend to work best to our eyes, because our eyes have red, green, and blue receptors.