I bought some hp mini PCs a while ago and they had the 3 pin design. As I understand it the third pin communicates the power output of the supply, so the device can either reject the supply or work in a lower power mode. Luckily though they just use a simple resistor to do the communication, so the fix was to just solder in a resistor on the device side, and then I could use an ordinary laptop supply (with the right connector adapter).

Dell is much worse here. As far as I know their devices use a serial protocol on the third pin, and so it’s much harder to bypass it.