In their current incarnation, I don't quite know what they could do with the follow-on missions without simply rewriting half the mission generation algorithm.
Specifically, missions (and particularly the chained missions) suffer from a very "top down" development approach where the system was made to just churn out missions ad nauseam without consideration to why those missions exist. There's no reason behind the missions, no grand conspiracies, no story to be told, they are just missions. This follows through to chain missions, as they can't have any particular nuance to them as they can't continue a story that hasn't even been started.
In order to make chained missions actually tell a story, they first of all need to significantly improve the foundations of the BGS in order to give a "why" to every mission and occurrence. If a faction is issuing a mission for pilots to source a commodity, why are they doing that and why couldn't they just rely on the commodity markets? For a pirate massacre mission, what's going on that would require a mission rather than simply relying on normal bounty hunters; is there a particular set of pirates who recently escaped justice or has there been another faction financing pirates in the system?
Ideally, chained missions wouldn't even need to be made explicit as there should be a narrative connection between them. If you are tasked to source some synthetic reagents to a station without being detected, then asked to clandestinely deliver some nerve agents to another station, then it wouldn't take a genius to put two and two together. These implicitly chained missions could even come from different factions, as then another faction in the nerve agent receiving station could offer an urgent source and return mission to deliver advanced medicines to counteract the effects of a "local terror attack from an unknown source". These missions could then be made branching for the player via some kind of in-game communications, as they could tip off local authorities as to the source of the attack, or even just hand over the nerve agents to the station's authorities, all with different potential outcomes and effects on the BGS for various factions in the system.