No. You can't just buy for "three other people" under your MEMBER ID.
If that were the case I imagine the bots would have their day in multiple fake account scalper paradise and all hope would be lost for us mere mortals.
You need one unique member ID per entry into the epic waiting room. If you are abso-fucking-lutely LUCKY enough to get transferred to that now GLORIOUS registration page from the Epic waiting room hell, when the time to stop shaking from all the coffee you've been drinking finally comes, you can only enter YOUR assigned Member ID for the purchase of a badge, and add up to TWO additional Member IDs. That's it.
In my experience, if someone else gets to the registration page BEFORE you're able to, while you're still suffering through the cruel waiting room torture of bad jokes and spinning blue circles , and that kind, sweet, and generous angel on earth is able to buy you an available badge under THEIR 2 additional Member ID allowance while they are buying their own, you can still POTENTIALLY buy for 2 other member IDs IF you yourself somehow also reach the glorious registration page afterward.
You would still have to enter in your very own member ID to continue with the registration process. The page will not allow you to enter any other Member ID first that is not your own, the same one only you used to enter the waiting room in the first place. This is the only allowed scenario when you can buy for TWO OTHER people and no longer include a purchase for yourself---because you already have a badge in the system now, the one your friend just purchased for you a few minutes ago.
TL;DR No, you can't buy for "3 other people". Only you and two other hopeful nerds. If someone else already got you a badge under their account, you can only enter your own MEMBER ID when you get into registration, but you will only be able to buy for 2 other people that don't yet have badges.
I've been doing this since the first year this new complicated only process first pissed me off to no end.
I've been doing this since I walked up and paid cash at the door--on the day OF, when it was all sunshine and rainbows and free t-shirts no lines, easy parking under the convention for only ten damn bucks a day...and no Hall H tents... Ugh....so yeah, I'm pretty damn grumpy and a bit bitter beyond my years about it.
Good luck.