Okay, this is one that RK and I are doing right now. The thing is, ours is sort of an anthology series that all takes place in the same universe; The Nocturneverse.
What we've essentially done is introduce characters sort of one at a time from different games. We took the notes from the solo sessions we're playing and turned them into stories.
That means each character we're playing on our solo games (We're using World of Darkness/Chronicles of Darkness Second Edition as the setting so, our world but a darker underbelly of it) and our characters seem to have events that are coinciding. You have a party of four characters, that's already fairly gameable. I would say get your hands on something like
Amazing Adventures (might as well grab
Manual of Monsters too...they're free so why not?) and roll them as characters and then play the entire thing solo with something like Mythic GM Emulator and do some random rolling, see what kind of things they get into. Write that. The reason I recommend AA and MoM is because it's a universal game and you can pretty much do whatever you want with it, setting doesn't matter.
If they're starting out together, you already have an adventuring party of sorts. If not, then write about each of them separately and have a shared mission bring them together with them working out the bumps along the way. There again, the game itself would give you all the major events and you can write something to bring that adventure that happened in your mind to life on the page. If you have any questions or anything, feel free to reach out. Happy to help out in any way ya might need.
If you want to join in the fun of The Nocturneverse as practice, hey, jump in. Shoot, it's a big ol' honkin' open table. The more, the merrier.