I've got three copies of a vector in pure Cyan Magenta and Yellow colors. I wish to overlap them so that they merge to give a chromatic aberration effect letting a blackish color where they merge.
Sounds like you need the Multiply blend mode. Make them overlap, select them, and in the Transparency palette (Window > Transparency if it's not on the screen already) change 'Normal' to 'Multiply' in the drop down menu.
(if you ever need the opposite effect, e.g. green, red and blue combining to form white against a black background, you want Screen from the same menu)
This assumes that the vectors are all set up how you want. If you need blurred edges, try adding a blur effect from the Effect ('Photoshop effect') > Blur options.
If the vectors are solid colour and you need to fade them out in various places like varying intensities on a photo's colour plates, that's a tricky, complex procedure: you'd be best to look up gradient meshes and the mesh tool and be prepared for a lot of patient delicate work by hand.