You don't really need 4 PCIe x16 slots on your mainboard to connect 4 GPUs for mining.

PCIe is designed in such a way as to allow cards with big connectors like graphics cards which typically feature x16 connectors with less lanes like x8 or x4 or even only x1.

If you were wanting to play games or other actually graphic intensive stuff on your computer you would need the bandwith that comes with a proper PCIe x16 connection. For mining a PCIe x1 connection is sufficent since only a limited amount of data is tranferred back and forth on the PCIe bus.

So if your mainboard has 4 different PCIe slots you can in theory connect 4 different PCIe x16 cards to them and have them work fine for mining.

The only problem is making them fit. Physically cutting down on the connectors to make them fir is theoretically possible but practically a really bad idea.

There are PCIe risers that can help you with the problem of physically getting your cards to fit on the board. There are even PCIe risers that function as splitters and turn a single x16 slot into 4 x4 slots for example.

As far as the PCIe Bus is concerned the whole thing would not be a problem. However you still need a to power and cool the whole thing and that is more likely to end up being trouble.