It certainly wasn't my intention to offend or upset anyone, so I sincerely apologize if any was caused. I am just a very lazy typist.
Hopefully this response is more friendly and more informative answer as to my understanding and reasoning, however it is a lot more typing then my initial response.
I read your question to be could the P55 chipset theoretically support an 1156 socket processor that had 2 x PCI-E x16 slots.
This is my reasoning.
As the PCI-E slots go directly to the PCI-E controller in the CPU in all the diagrams of the P55 chipset that i have seen, then the interface from the CPU to the P55 chipset would be unaffected then I see no reason for it not to be supported.
All that should need to do is improve the PCI-E controller on the CPU to have more lanes connected, and have more PCI-E lanes routed on the motherboard.
We are not talking about changing the DMI link here, just the PCI-E controller which you said in the question in onchip, and daegan pointed out in his answer as well that the PCI-E controller is ondie in the CPU.
http://techreport.com/articles.x/17513
Is a review that I read of the P55 chipset which shows the memory controller and PCI-E 2.0 controller in the CPU, in that the PCI-E 2.0 and RAM slots goto the CPU and not the P55 chipset.
The diagram of the chipset layout is the same one as on the Intel site, so I have no reason to doubt the diagram in the article.
From the diagram then unless I am missing something then data transfer from the CPU to system memory and GPU doesn't seem to route via the P55 chipset at all, as the PCI-E lanes seem to go direct to a PCI-E controller in the CPU and the memory controller is located in the CPU as well.
The article I linked to does raise the question of wether the 2Gb/s DMI link would be enough, however as the x58 and ICH10 have the same DMI link speed then if the data transfer from the ICH10 is enough for 2 x PCI-E x16 slot system then I see no reason why the 2Gb DMI link on the P55 would not be able to support such a PCI-E configuration.
All that the x58 IOH does is provide the PCI-E links for the x16 slots with a QPI link to the CPU at 25.6GBs however, from the X58 to the ICH10 is a 2GBs DMI link, the same as the 1156 CPU to the P55 chipset.
Whilst the ICH10 has the following
12 USB ports vs 14 for the P55.
6 PCI-E x1 slots vs 8 for the P55
Audio is the same, SATA ports are the same, both have Gigabit LAN but admittedly different connections into the chip.
If the ICH10 can provide enough data from storage, network and audio over a 2GBs DMI link then I cannot see how the P55 cannot provide enough over the same DMI link to support a system with 2 x PCI-E 2.0 x16 slots.
The DMI link not having to provide bandwidth for CPU to GPU or Memory, from what I can see on the diagrams.
However if I am mistaken in my understanding of the memory and gpu data transfer paths to the CPU then I am more then happy to be corrected, however I cannot see why Intel would route traffic down to the P55 chipset and back again from the ondie PCI-E controller or from the ondie memory controller to the other parts of the CPU.
I merely added the second part as to why I can't see Intel releasing such a chip, and was more for the original thread starter who initially believed that the i7 on 1156 may support 2 x PCI-E x16 slots at full x16, pointing out why such a chip would be unlikely, so I did see this as a valid point in the overall thread.
Again my apology to anyone that I unintentionally may have offended or upset with my first response.