With cyan and magenta only it's not a problem. Just make sure that your design contains no black or yellow. Use the Color and Swatches panels to produce and store mixtures of cyan and magenta for colouring your design elements.
But in your headline you say "spot color screens" which is a bit more complex because Illie can't store mixes of spot colours as swatches.
So you will have to work with overprints and have Overprint Preview turned on while you work.
The other possibility is to work in false colours, using say magenta for spot red and cyan for spot blue.
There's nothing to prevent you from working this way and I have occasionally done so, but you will need to explain carefully to your printer what you are doing and it's not a bad idea to add a colour legend to your artwork to ensure that your false process colors are printed in the right spot inks.
And by the way there's no need to work on separate layers. Just let Illie's stacking system work on its own.
It is a not uncommon misconception with beginners that each colour of a separation should be on a separate layer.
Another thing: If you need to use white for blocking things out, that's quite o.k.
Use preferably greyscale or process white rather than 0% of spot colours, and DON'T set white to overprint.
If you do it will disappear as you will see by turning on Overprint Preview.