Here's how it works (in my game, anyway). When you get to removing the sigil stone from an Oblivion Gate, look at it carefully. You will see what appears to be a core at its centre. Activate at this spot. Normally, when you activate a sigil stone once, the 'activate' hand disappears, right? Well, I've discovered that if you activate in the right place (around the middle 'core'), the 'activate' hand will remain and you can keep activating the stone to gain two additional sigil stones. If it doesn't work initially, try reloading and activating in a slightly different area of the stone, it is modestly difficult to locate the optimum area but very possible.
I am uncertain whether this would work for other people too, or if it is just weird (but nice) bug with my game. Please try it and let me know!
Edit: well, just noticed the wiki actually does note it, albeit rather unceremoniously at the bottom of the page. Damn, I thought I'd made a great discovery!