That's tricky. Maybe duplicate the objects a couple of times, and play around with the intersection boolean and a difference boolean operations until u got all parts u need to make the whole again.
With nurbs u could've duplicated a curve from one object and projected it onto another.
U'd think Maya would have a function that cuts at the intersection of 2 polygon-objects without losing parts like in boolean. I came across this myself a couple of times. I think 3DS Max has this and so Discreet will surely implement this eventually in Maya too.