iOS - Clipping union of two paths using UIBezierPa

I'm attempting the create a clipping path in the shape of a plus sign, so that subsequent paths that I draw into the same context have this portion removed. I create the clipping path using two rectangle paths overlaid on each other.

This is what I'd like the final drawing to look like when I subsequently draw a circle:

      xXX|   |XXx
   XXXX|   |XXXX
XXXXX|   |XXXXX
———      ———
———      ———
XXXXX|   |XXXXX
   XXXX|   |XXXX
      xXX|   |XXx

However, it actually looks like this:

      xXX|   |XXx
   XXXX|   |XXXX
XXXXX|   |XXXXX
——— XX———
——— XX———
XXXXX|   |XXXXX
   XXXX|   |XXXX
      xXX|   |XXx

If I read this behaviour correctly, the intersection of the two rectangle paths is not forming part of the clipping mask.

It seems (not surprisingly) that appendPath does not create a single unified path from my two rectangle paths in this case - I'm assuming that there is nothing I can do about this. Furthermore, Core Graphics doesn't seem to have any functions relating to path unions etc.

Does anyone have any idea what I can do? I've included the relevant code snippet.

Drawing the plus sign using one path isn't a solution, as I want to add other overlapping paths to my clipping mask.

        CGContextSaveGState(context);

        // create clipping path
        UIBezierPath *clippingPath = [UIBezierPath bezierPath];
        clippingPath = [UIBezierPath bezierPathWithRect:CGRectMake(centrePoint.x - 2.0f, 0.0f, 4.0f, self.sizeY)];
        [clippingPath appendPath:[UIBezierPath bezierPathWithRect:CGRectMake(0.0f, centrePoint.y - 2.0f, self.sizeX, 4.0f)]];

        // use the clipping path to create a hole in the context
        CGContextAddPath(context, clippingPath.CGPath);
        CGRect boundingRect = CGContextGetClipBoundingBox(context);
        CGContextAddRect(context, boundingRect);
        CGContextEOClip(context);

        // draw the icon shape (clipped portion is removed)
        iconBezierPath = [UIBezierPath bezierPathWithOvalInRect:CGRectMake(self.sizeX / 3.0f, self.sizeY / 2.25f, self.sizeX / 3.0f, self.sizeX / 3.0f)];

        [highlightColor setFill];
        [iconBezierPath fill];
        CGContextRestoreGState(context);

You can add back the piece that gets knocked out by the intersection using CGRectIntersection

    CGContextSaveGState(context);

    CGRect rect1 = CGRectMake(centrePoint.x - 2.0f, 0.0f, 4.0f, self.sizeY);
    CGRect rect2 = CGRectMake(0.0f, centrePoint.y - 2.0f, self.sizeX, 4.0f);
    CGRect rect3 = CGRectIntersection(rect1, rect2);

    CGContextAddRect(context, rect1);
    CGContextAddRect(context, rect2);
    CGContextAddRect(context, rect3);

    CGRect boundingRect = CGContextGetClipBoundingBox(context);
    CGContextAddRect(context, boundingRect);
    CGContextEOClip(context);

        // draw the icon shape (clipped portion is removed)
    iconBezierPath = [UIBezierPath bezierPathWithOvalInRect:CGRectMake(self.sizeX / 3.0f, self.sizeY / 2.25f, self.sizeX / 3.0f, self.sizeX / 3.0f)];

    [highlightColor setFill];
    [iconBezierPath fill];

    CGContextRestoreGState(context);

This satisfies the requirements of your question, but whether it entirely satisfies your needs depends on the nature of the "other overlapping paths".