When you check the schematics, you will notice that there is also a pin 5 on Amiga ports for a third button or middle mouse button.
Indeed. The interesting thing about buttons 2 & 3 is that these pins are writable as well as readable, so they can be used for multiplexing to give you even more buttons. Presumably this is how the CD32 pad works. The Sega Megadrive pads also work this way, but unfortunately they use pin 7 as the select line, which on the Amiga is +5V. On the Sega pads, +5V is on pin 5. So if you swapped pins 5 & 7 in theory you could use all of the buttons. But it doesn't work the same way as the CD32 pad, which apparently has some sort of state machine inside it.
I have wanted to make myself an adapter for some time to get the use of those extra buttons. Having only one button to play with is really frustrating from a game design point of view. (It's one reason Mr Beanbag's only move is jump!)