What like. Genre are your friends interested in? To be honest I can't think of any other game like SS13, so if you want that only with less terrible graphics and less being on byond you will be pretty much be outa luck. Probably. Multiplayer simulation arn't really a thing that exists for the most part outside of ss13. On the other hand if you like the hidden role aspect you could try the mafia section of fg&rp. Which is sorta like the traitor thing in ss13 only played on a forum.
On the other hand, if you just want to play ftp games with your friends, warframe, dota2, and path of exile are all good.
Warframe is a FTP FPS, although I didn't get far into it because I am not a fps player, it seemed good from what I played, although I have been told it gets grindy/repetitive later? So you will have to like the gameplay. (Although I'd argue that's not really a weakness persay.)
Dota2 is probably doesn't need a introduction, but in case you don't now it's a free moba game, it sure is stealing away a hour or two every day for me and my friends currently. It's also probably one of the freeiest mainstream games there is.
Path of Exile is a FTP game that's a lot like Diablo 2. It's got a very nice business model (I sometimes wonder how they can make enough money on it, it might be almost as free as dota). I'm not really sure if I liked it as much as Diablo 2 to be honest, but it's hard to argue with it's price and it's still a very fun game. I personally found it a little short (although I've not actually finished it yet, but I know I am close) so it might not last your friends all summer if you only play the game though once and don't replay it on the higher levels. (How it works is you play though the campaign though three times, each time at higher levels and higher difficulties, and then you eventually get the ability to make randomly generated dungeons with random traits. Although all the levels of the campaign are also randomly generated, but not with random traits.)
These are sorta the first three that sprung to my mind. All of them free and fun and all very different. So I hope at least one is to your fancy.