I recently discovered that you can put a PCIe x4 card in a x8 or x16 slot.
With that said, what would happen if you took multiple PCIe SSDs and shoved them all into a 16x PCIe slot?
Nothing... The PCIE key slot would prevent a card being inserted anywhere except the front of the bus. Therefore, only one card can be entered in a slot at a time. If you were to remove the key, you may end up damaging your cards and/or your board.
The PCIE key is the first few pins, followed by a gap, and then the rest of the pins.
The computer would most likely not boot. It might short out.
See, a PCI x4 slot is not four as large as an x1 slot.
All PCI-e connectors have a shared layout: The first 18 pairs of connectors are for power supply, SMbus and JTAG communications, clock sync etc. Only then come the data pairs. This means there is only one way to correctly connect them.
Any second card in the same slot would at best connect (and not be able to use) the remaining data pairs. That is at best. At worst you'll connect its pins in an unexpected way, e.g. connecting the possible joined +12 power lines to differential signal paths. That will cause a short.
For more details on its pinout, please see Wikipedia: PCI Express.
Note that PCI-e bridges exist. You could put an x8 bridge card in an x8 (or bigger) slot and (via active hardware on that card) present two x4 slots, each with its own connector.