Trust me, I really cannot name other VNs like this, not without ruining the surprise for you. The only one I can name is Saya no Uta because the game gets dark in the very first seconds, so you're not really spoiled for knowing that one. It's also on the short end, about the same length as DDLC, so it's not a massive 40 hours long VN like Clannad.
What you can do however is take a recommendation chart from here, pick a random game in it and play it. The very first one is pretty good: you can pick any game in the blue field, you cannot go wrong. There are at very least 3 VNs in there which have the same twist as DDLC. There are also nukige (basically porn games) like Wanko to Kurasou in there, but if you can withstand the adult content even those games have twists that can be real tearjerkers.
Have fun.
P.S.: Keep in mind that most VNs have the One True Route, which basically means that after you complete the game, a final route unlocks which reveals all the secrets of the game. You may want to use a spoiler-free walkthrough if you have problems with these kind of games.
RE: Everything is not Doki Doki in the Literature Club