Currently, the punch designix can do both || and && systems to assemble cards.
However, according to the Homestuck series itself, the || system is done by punching together 2 cards at once in the designix, and the && by inserting 2 cards at once in the lathe's card slot.

I suggest to restrict && to the lathe for coherence, but I'll understand if this suggestion is refused to siplify the gameplay (or to make the player need shale grist for both combinations).

I am planning on changing that sometime in the future, at the same time as making the machines multiblocks. You can on the other hand already double-punch a card to perform || alchemy.

Yeah, the || alchemy is correctly placed, it's just the && one that bugs me being on the wrong device...

Just so you know, I'm working on this right now on the 1.8 branch.