As samisnake says: the Z77 boards have PCI via PCIe->PCI bridge (why did you ask for "native"?). But in any case the most PCI slots I've noticed on any Z77 boards is 2.
You need to go to the manufacturers' websites and do a survey of all the models they have. You may find something, such as the
Gigabyte GA-P75-D3P. I'm not aware of anyone who's done a build with it, although I think at least one person has used the GA-P75-D3 (no P). Both of these boards have
four PCI slots (directly driven by the B75 chipset) and from the look of the specs I would expect their Ethernet, HD4000 video, USB2, USB3, and SATA ports to be supported. Actually, I'm not sure what the difference between the boards is supposed to be.
There was a reported issue with the audio driver (back in November) on one board, but it's unclear whether that was user/software error which shouldn't happen again.
Check through all the Gigabyte boards, and while you're at it check the Asus, Zotac, MSI, etc boards as well.