See
Poul Anderson's Future Histories.
Maurai: post-nuclear-war Earth
Flying Mountains: asteroid colonization
Rustum: extra-solar colonization
Kith: interstellar trade
These four series sound like successive stages of a single sequence. Indeed, the asterites (asteroidal colonials) begin extra-solar colonization at the end of Tales Of The Flying Mountains. But it is not Rustum that they set out to colonize. These are four alternative timelines. However, a single future history can incorporate a Terrestrial future, staged extraterrestrial colonization and inter-systemic contact/communication/commerce. Thus, in Anderson's Psychotechnic History:
post-nuclear-war Earth
colonization of Mars and Venus
colonization of extra-solar planets, including Nerthus
the Stellar Union and its Coordination Service
Technic History:
The Chaos on Earth (off-stage)
exploration of the Solar System
the Grand Survey of extra-solar planets
the Solar Commonwealth, the Polesotechnic League and their successors
The Psychotechnic and Technic Histories demonstrate two ways to construct a future history series.
Psychotechnic: Follow Heinlein by compiling a future history time chart, then fit a series of stories into successive periods of the chart.
Technic: Link two previously independent series, then explain what happened between them. Why does Technic civilization have an early period of commercial expansion and a later period of imperial decline?
The two remaining future histories:
Harvest Of Stars: human-AI interaction.
Genesis: post-human AI.
These also sound like successive stages although they are alternative histories but they present ideas that could be combined with the other ingredients into one comprehensive future history series.