For a scripted set of missions with lore, I think Ram Tah is all we've currently got. Galnet and the COmmunity Goals / Interstellar Initiatives ocasionally had some plotlines and were ocasioanlly linked to PowerPlay characters, but they were temporary week-by-week or at best month-by-month things; all that's left of them is the Galnet archive.
You will occasionally get given a "chained mission" - if you successfully complete a high-value mission for a faction, they might give you a second, usually more lucrative mission. Trouble is, these missions aren't logically connected to the precursor mission - though the procedural generator tries hard. Example: I successfully complete a cargo-delivery or donation mission and I'll be given a mission chain. Sometimes it's "deliver these two or three tonnes of cargo for several million credits"; more often than not, it's "go and assassinate these people for us". I'm an explorer doing part-time space-truck driver and courier guy work, I don't know why they think I'd make a good assassin. And that, I think, is it - no multiple-link-chain mission series, no significant reward when a chain is complete.
Personally, the kind of chain mission I'd like to see is a chain to support a small, struggling colony that nobody ever visits. "Bring us this list of urgent supplies". You bring the list, maybe they throw in a "stop this pirate from harassing us" or something else, and at the end of the chain, there's a tangible uptick in the colony's wellbeing - perhaps an increase in population, perhaps a change in economy type from "colony" to something else. Right now, the closest thing we have to this sort of thing is the "station repair" mechanism - which is far too big, too slow and too tedious to qualify, requiring millions of tonnes of cargo to be shipped, with the eventual reward - the restoration of a fully functional space station - nowhere near compensation enough for the majority of players.
MIlitary chain-missions are another possible option to add, to help flesh out the much-neglected "military career path". Go and steal this data for us. Right, the data shows us they've got a secret weapons research base over there on that planet, we want you to take the base out. Well done, but now it appears their chief researcher escaped from the ruins of the base and we need you to hunt her down. That kind of thing, at the end of which you might get a nice shiny medal to pin to your holo-me chest, as well as a significant rank-boost.