Hi hutha,
I do have an idea for how this would work with three players; it was a stretch goal that we didn't meet during the Kickstarter for The Almanac of Sanguine Paths (aka "werewolf Dead Letter Society", which is compatible with DLS). In that case, the third player takes on the role of someone working at the Society.
If I were making it myself, I'd give them their own set of tarot card prompts, distinct from those of the vampires. However, to approximate it you'd pass your letters through that third person, and they'd be able to take liberties with what you write and use it for their own purposes.
As for more than three, it's tricky -- it strays into territory that's out of scope for this game. There's certainly nothing stopping you playing two games side-by-side (e.g. A writes to B, and C writes to D), and collaborating on the events of your games together, though I expect you'll need to talk more 'out of game' to maintain world consistency.
Alternatively, you could try having one character write to two others, for example, if you have players A, B, C, and D, then:
A writes to B and C (start in Letter Phase)
B writes to A and D (start in Society Phase)
C writes to A and D (start in Society Phase)
D writes to B and C (start in Letter Phase)
then for the gameplay loop, write two letters in the Letter Phase, and continue with the Society & Chronicle Phases as usual (but receive two letters instead of one during the Chronicle Phase). You probably want to use more than three Chronicle Points during the Chronicle Phase, as it's going to take lots more time for someone to write two letters than one, and you'll end up with more things you want to explore as a result of it. Whatever number you pick, make sure everyone gets the same number of opportunities. (My gut feeling is that six points, while the obvious number, might be too many. I'd be more inclined to try four first.)
If you give this a try, communication between you all is going to be key. I could see four players left to their own journaling coming up with more conflicting ideas to resolve than when it's just two.
I'd be really curious to hear the outcome if you try it!
Still, Dead Letter Society (to me) has been about a personal connection between two vampires aided by a shady society. If you're after something more akin to vampires meeting on a forum/group chat to discuss things, or in person, I think that's heading into different game territory.