The gigabyte gaming 3 and gaming 5 do. Since they're not packed with a billion SATA and USB ports, there's lots of PCIE lanes left.
PCIE1 runs at 16x if there's nothing in PCIE2. Both run at 8x if there's two cards.
But with PCIE 3, its a choice between using it as x4, or using the 4 1x slots. I've got no need for the x1 slots, so I'm fine with that tradeoff.
It's a great configuration - you can run a physx card or a full speed nvme SSD in the x4 slot without affecting the bandwidth of the other two slots.
And they're inexpensive boards too, like $150ish. As far as I can tell, the only thing the 5 offers over the 3 is higher quality caps and gold plating on the audio jacks.
I don't have the board, just going by the spec sheets:
1 x PCI Express x16 slot, running at x16 (PCIEX16)
* For optimum performance, if only one PCI Express graphics card is to be installed, be sure to install it in the PCIEX16 slot.
1 x PCI Express x16 slot, running at x8 (PCIEX8)
* The PCIEX8 slot shares bandwidth with the PCIEX16 slot. When the PCIEX8 slot is populated, the PCIEX16 slot will operate at up to x8 mode. (The PCIEX16 and PCIEX8 slots conform to PCI Express 3.0 standard.)
1 x PCI Express x16 slot, running at x4 (PCIEX4)
* The PCIEX4 slot shares bandwidth with all PCI Express x1 slots. All PCI Express x1 slots will become unavailable when a PCIe x4 expansion card is installed.
* When installing a x8 or above card in the PCIEX4 slot, make sure to set PCIE Slot Configuration (PCH) in BIOS Setup to x4. (Refer to Chapter 2, "BIOS Setup," "Peripherals," for more information.)
3 x PCI Express x1 slots
(The PCIEX4 and PCI Express x1 slots conform to PCI Express 2.0 standard.)
1 x PCI slot