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I'm not sure if you understand the basics of an arcade cab setup.
Hope I can help out a little. When someone says one-slot or four-slot, they're referring to the motherboard or MVS board. If you're playing a home game, this would be like the Nintendo console or whatever. Into that goes the cartridge which is the software. The amount of slots refers to how many cartridges the board can accept at one time.
For all this to work, the board with cartridge plugged in just needs a power supply, monitor and controls hooked up. That's all there is to it.
A Neo Geo cab will have only one motherboard or deck. It's either 1-slot 2-slot or 4-slot. They can be swapped, but not combined or anything else.
It sounds like your cab may still have a 4-slot board with just one cartridge in it. Open the sucker up and just see if the board has 3 empty cartridge slots. If so, you probably don't have to do anything but get some new MVS carts and load it up.