I can only use 3 screens (colours) for a degree module and was wondering can i merge a copy of the key(K) layer to each of the CM and Y(cyan, magenta and yellow) layers in Photoshop so when they are layered onto the paper they will add a darker colour replacing the black? Thanks
Technically, you can but it's a bit messy and you need to mention to the printer your intention.
Using only CMY to replace black is a common technique used for skin tones or projects like wedding dress catalogs (with light or pastel colors).
It's not so common to replace entirely a black though but technically it's not worse than mixing any other inks together to get a dark navy blue or brown, for example. It will look like a very dark rich gray, almost black. It might even look very stylish actually. In fact, using black ink only looks dark gray when printed...
The main downside to this is that your project will take more time to dry and you should also avoid using that "black mix" on large areas of your design.
A suggestion: it's better to have a bit more cyan than yellow+magenta in your CMY recipe. This way it will look like a very dark metallic gray and there's less chance it will look brown. It will also help for the total color density by lowering it a bit.
Examples of black and CMY black;:
Not a huge difference if you cannot use more than 3 color separations. Note: the 100% black in reality is more grayish once printed. Also note how the last recipe with more Cyan looks more gray.