It's possible, as of v0.18! I read about it on uboachan.net (and I was going to post a link to the relevant thread, but apparently my karma is too low). You have to eat cake at the Sugar Hole 10 times. This is extremely tedious - you first need to raise 3000 yen, and then walk to the Sugar Hole ten times, as you can only eat the cake once per dream (on the bright side, you'll obtain the sugar menu as a side-effect of eating all that cake!). I didn't time how long it took me, but I'd guess it was more than an hour overall. :( After eating the tenth cake, from your next dream onwards, you can make the cone disappear by interacting with any of the maids. Thankfully, this still works if you save the game and reload it later, so you only need to slog through the endless cake-eating once.
I don't want to post a spoiler about exactly what is at the top of the stairs, but it seems to be a part of the game that hasn't been finished. The room you reach doesn't have an exit (even though it looks as though it should). The images relating to the new room can be found in the usual location for room backgrounds in the game's data files (the Panorama folder). Note that the room behaves slightly differently if you escape using the Arm effet and then go back to it again.
I've already edited the Apartments page of the wiki to mention this. Maybe we should change the Sugar Hole page and the Extras page too? I can't be bothered, tbh.
I'm going to post to the theories thread about this, as what I found at the top of the stairs doesn't fit into my existing theories on the game!