Polygon overlay with Shapely

You need to iterate at some level. (Update: I've edited to remove all "for" loops, except for one list comprehension)

# imports used throughout this example
from shapely.geometry import Point
from shapely.ops import cascaded_union
from itertools import combinations

# Here are your input shapes (circles A, B, C)
A = Point(3, 6).buffer(4)
B = Point(6, 2).buffer(4)
C = Point(1, 2).buffer(4)

# list the shapes so they are iterable
shapes = [A, B, C]

First you need the union of all intersections (use a cascaded union), using the combination pair of each shape. Then you remove (via difference) the intersections from the union of all shapes.

# All intersections
inter = cascaded_union([pair[0].intersection(pair[1]) for pair in combinations(shapes, 2)])
# Remove from union of all shapes
nonoverlap = cascaded_union(shapes).difference(inter)

Here is what nonoverlap looks like (via JTS Test Builder):