What we know
Very little! Based on the teaser poster to the right, the release date is September 27th, 2024, almost exactly a year after the release of Saw X. Kevin Greutert is returning as the director from Saw X and will presumably edit it as he did that film and most of the previous Saw movies. Patrick Melton and Marcus Dunstan, writers of IV, V, VI and 3D, are returning as the screenwriters for XI. Filming is scheduled to start sometime in March - and that's all we know for now!'
My speculation
Based on the success of Saw X as a kind-of standalone movie (it functions pretty well as a film even if you have never seen any Saw movies before, and made nearly ten times its budget at the box office), I would be very surprised if XI did not follow that formula. My prediction is it will take place after X but before II - and keep the focus primarily on John and Amanda. I also would expect Cecilia to make a return, as she was one of the standout characters. Will she be tested again? If this were an earlier Saw sequel, I'd say no; she's been tested, she played the game and she passed. But, if Lionsgate does draw heavy inspiration from X, and distance XI from the rest of the sequels, then I wouldn't be surprised if John's philosophy gets a little... muddier. Cecilia was 1) such a captivating character 2) so unlikeable and 3) so glib about bending the rules of her test. Plus, X left off on her surviving and acting basically as if she "won" - so Saw XI might include her facing another test, to make for a more satisfying conclusion for fans of X - even if it's a little out of character for John.
Or, who knows, maybe she'll even become an apprentice! It seems unlikely but nothing is impossible in these movies, and if Lionsgate is committed to her as a core character than I think she would be a SUPER interesting addition to the apprentice dynamics... every apprentice bends the rules and diverges from John's philosophy with their traps but I have to imagine Cecilia would take that to a whole new level as an apprentice. Plus, that would be a classic end-of-movie twist for people whose first Saw movie was X, and might not be familiar with apprentices or the usual twists.
Moving on from Cecilia, though, my overall prediction is that XI will generally follow X in visual style, structure, and the smaller focus on a few victims. A police investigation B-plot seems unlikely but not impossible, and I'd expect very little connection to Hoffman or Dr. Gordon. I think the focus will be kept on John and Amanda's relationship, as they run a new gauntlet or series of traps which take up most of the focus of the movie - potentially with Cecilia as an apprentice, a victim, or some kind of rival.
My hopes / ideas
That's what I think is most likely to happen in Saw XI - but it's not what I'd most like to see. Most of these are completley unreasonable and basically guaranteed not to happen but if we're talking hopes and dreams, the way that Saw X acts as kind of a prequel-bridge between Saw I and Saw II (kind of a Saw 1.5) has me excited about the possibilities, so here are a few of my ideas.
Saw 3.5
The way that III and IV overlap has always seemed messy to me. It's probably the single messiest bit of the timeline, in my opinion, and the plots of the two movies are, really, almost completely disconnected. This might just be an excuse for me to beg for a Peter Strahm appearance, which I think is absolutely never going to happen, but on the other hand this might be a good way to expand a little more on what happens after Amanda's death, even with some flashbacks to Saw III and before (since X put a lot of emphasis on her character)? This applies to the idea of a Saw 2.5, too, which could be a heavily Amanda-focused movie.
Saw 4.5
This is probably the least likely one on this list, but also the one I'd want to see most. I'm a sicko and a freak, so my favorite characters are obviously Hoffman and Strahm. Admittedly I think IV and V fit pretty well together as a pair, probably better than III and IV, or VI and 3D, so there's really not much need for something between them. But Hoffman and Strahm's cat-and-mouse game (and obviously their world-shattering gay romance that's happening just off screen I swear) is really my favorite part of the franchise. So I'd be excited to see any additional bits of story that could be told about them in this timeframe. Plus, this could help smooth the jump from Rigg being the POV cop character to Strahm.
Saw 5.5
Continuing with the implausible Hoffman-focused movies, I've never fully grasped the timeline of him being found out as a Jigsaw apprentice. I think it would be interesting to see how exactly his whole charade with Strahm's severed hand falls apart, maybe even focusing on Perez (my beloved) investigating him leading up to her death in VI.
Saw 8
I want to know what happens to Hoffman after the cliffhanger ending of 3D, damnit! Does Lawrence really leave him to die in the bathroom? Does that mean Lawrence is taking over as Jigsaw, or not going to run any traps? Who were the pigheads helping him? And, hey, can we get a little more information on him as an apprentice? That could really fit into any of the ideas in this list,since he was apparently there from the start. In any case, I'd like to think something taking place after 3D will happen eventually, but I doubt it'll be the immediate followup to X.
Like I said, I don't think any of these ideas are likely. But because this franchise is so loose with the timeline, there are really infinite stories you could squeeze in between or even during other movies (again, the precedent set by III and IV has had disastrous effects on the kind of fucked-up fanservice Saw movies I can conjure up). So who knows! Right now, it seems very likely the franchise is going to focus in on John and Amanda as the core characters, perhaps Cecilia as the third, and only drop occasional hints to the wider lore. But there's plenty of room for movies with a similar tight focus on Hoffman, or Strahm, or Perez, or especially Lawrence. In fact, a movie that just focuses on Lawrence's "career" as an apprentice, spanning the timeline of some or all of the mainline movies, would be very interesting. So who knows. Maybe in the future, the franchise will focus in on some other set of characters. Whatever happens, I can guarantee I'll be there to see it!