Using PiFace but still using I2C

I got a PiFace Display in the mail not too long ago, and just cracked it open.
I got it as a tester to write a review, because I wanted the LED display and the infrared on it.

I thought it could connect by using jumper wires, but it overlays ALL of the Raspi's GPIO pins.
The PiFace has 8 output pins, but I've read they are connected to the PiFace's chip on the 3.3v line.

So, the problems I face are that I need to have my PicAxe board connected via I2C.
That means I need 6 wires going to it: 3.3v, 5v, 2 grounds, and the RXD/TXD wires.
I may also want to connect an additional bluetooth module to it's serial (3 wires).
I'm still not an expert in this scene compared to many of you, so I'm not all what's out there.
I was thinking the cobbler might work, but I'm not sure.

For one, I thoguht that would be a lot of male-to-male jumpers, because I want the PiFace mounted on the body, not directly on the Raspi or breadboard. Would there be a working ribbon for that?
But my bigger question is, is there anything that would stop this ideas from even working? 

Not sure if my question is clear enough or not, got about 20 ideas bouncing around in my brain right right, but I'm still a bit fluff coming to this, so thought I could get better expertise without spitting out more ideas that may or not make sense.


Edit: Here's an image of the PiFace Display Module, with the problem front right.

The method it connects to the RPi is the black box (forget what it's called?),
which connects to all the GPIO pins on the board (13x2 pins).

So, if I got a cobbler, is there a way to look up 13x2 Male to Female jumper, or should I use jumpers at the end of a female to female cable, and would it work, or is there something I'm missing?

Thanks for the responses!

I initially decided to get more header pins, and run an 40-pin IDE cable (ignoring the overhang).

However, the item included in your reply gave me a great idea, using that item.
As I said, I don’t want the PiFace directly on the Pi, but mounted somewhere it could actually be used.
So, I decided to get a Cobbler Kit (GPIO/26-pin) extention cable.

What I plan to do, is take that stacking header you listed Maxhirez, put it onto the existing GPIO pins to create more room.
At the baseof the header, I’ll to put jumpers (shunts) out to the side of each pin, to connect each wire to from the sides.
From the main pins, atop of those shunts, I’ll put the extention ribbon (male to female), to go to the PiFace on the head.

 6677, thanks a lot for your info, too! In this case, I’ll already have those holes overlapped by jumpers.
However, would you happen to know where the documentation is for which of those holes are for what? 
Because I really only NEED the 3.3v, 5v, 2 grounds, and 2 I2C pins free.
However, know if it’s possible to connect multiple objects to the serial bus?

Thanks again for the help!