Okay, some thoughts on the contents of the system, which I'll admit are largely, though not entirely, inspired by browsing Wikipedia. This got really long, so I've summarized my suggestions at the end.
Let's assume that
http://arxiv.org/abs/1504.07065 is correct in stating that the system formed 9-10 billion years ago by fragmentation from a single protostellar disk. That means it's quite old, so there's a decent chance it's poorer in metals than the sun. In particular, likely to have fewer of the products of Type Ia supernovae (notably iron) but not quite as depleted an amount of Type II supernova products (the alpha elements), which information I'm getting from Wikipedia, so it's not entirely clear how reliable this is. Now, I've found elsewhere that we have found some really old planetary systems, including one with five planets very close to the star. An article I found somewhere online, but neglected to save the link, suggests that metal poor stars are likely to form planets closer to the star, but not as many farther away, because planet formation takes longer, so the far away ones lose the protoplanetary disk before they can form. Wikipedia's article on planet formation suggests, furthermore, that metallicity has a higher effect on whether or not large planets get to form, and less so on smaller planets. So we may be looking at a system that consists largely of smaller bodies. This article also suggests that gas giants influence inner planets by encouraging fewer, larger bodies.
Now, if we look at the detached binary, which has the additional star associated with it, this additional star is perturbing away much of the outer system past the frost line, though there's still some room. Taking all these factors together, I would suggest that this inhibited the formation of large bodies in the detached binary's outer system. Instead, this outer system formed an icy asteroid belt, one which extends farther than ours, with a higher total mass, but fewer dense elements. Maybe a couple of dwarf planets there. Nowhere near the extend of, say, the Kuiper Belt, however. Closer in, rocky bodies managed to reach more substantial size and clear some orbits; with density likely to be higher closer to the star, a couple of decent planets intermediate between Mercury and Mars that are in close orbits, followed by a few barely-planets in intermediate orbits. Those may be quite eccentric due to all the perturbations from having three stars in close proximity, with the farthest approaching the frost line. Maybe the barely-planets could be dwarf planets instead. If the detached binary used to have a somewhat wider orbit, at least around when it formed, potentially that could contribute to the system's scarcity, and also encourage eccentricity when it evolved. So this could be a good system for lots of habits. Volatiles might be a bit scarcer, too, what with the comparative lack of material beyond the frost line, but maybe all the eccentricity would've spread them around more.
The extra star associated with them would be a bit less chaotic, and have had more room beyond the frost line, though still not a lot. Small terrestrial planets and an icy nebulous panthalassic, maybe? With small tide-differentiated moons?
The contact binary has a lot more room, so it could have the potential to be somewhat more conventional. Orbits closer to circular and all that. More volatiles. Potential for planets that aren't so tiny. On the model of the known very old system, maybe there'll be a planet that orbits particularly close to the contact, which may even be one of the more massive terrestrial bodies of the system. No natural garden worlds, and considering the scarcity of iron and the age of the system, probably nothing with much plate tectonics, but there could be something like a somewhat more habitable Mars, which may harbor microbes. And then trailing off a bit, maybe a gas dwarf or two, then some ice balls, then just a scattering like the Kuiper Belt. Though I don't think planets would extend as far, really. Not as much material, nor as much incentive for migrating outwards.
However, one monkey wrench which would affect this proposal, and might be quite exciting to boot! Apparently fragmentation is one theory of a possible trigger for the formation of brown dwarfs and gas giants, which is probably rarer than accretion, but this system already probably went through fragmentation to form all these separate stars! Adding in a brown dwarf might be excessive, but a fragmented gas giant, maybe even a superjovian, could be exciting. Without as dense a protoplanetary disk, it might not be inclined to spiral inwards, so it might just stay orbiting around either in the distant reaches around the contact binary, or possibly around the other three, or even one at both places. If both, I'd suggest the former be superjovian, being as there's less disruption in that environment, and it could be closer to a star, and the latter be more like a Neptune. They could be good places for bubblehabs, which I hear are underrepresented, especially the smaller one, which would have a more agreeable gravity. They'd have potential for moons, especially the big one, which could have captured some of the planetesimals/dwarf planets, and maybe have room for something Mars like in size from its own accretion disk, though totally frigid.
Summary of my suggestions:
Contact binary: Epistellar superhot Earth-sized planet, almost certainly tide-locked, no atmosphere, probably molten on the day side, good view but not good real estate. A few smaller Terrestrial planets, including one in the habitable zone which is a good candidate for terraforming, with native microbial life, sort of intermediate between Earth and Mars, with very small core, barely any iron, and largely tectonically dead. A gas dwarf, an ice ball or two, and then a bunch of smaller bodies, like the Kuiper Belt... until, fairly far out, there's a superjovian with its own frigid moons, including one close to Mars in size.
Detached binary: Nothing bigger than Mars. A couple of planets close to the star; farther out, the planets get increasingly smaller and more eccentric in their orbits. Eventually it becomes an asteroid belt, with some dwarf planets, generally very eccentric. Poor in volatiles and iron. Plenty of carbon, I guess? Anyway, settlement would be likelier to involve habs than just settling the planets, meeting that design goal. (Maybe this could go to someone other than the Solar Dominion, like the Deeper Covenant or something, even though they're not red dwarfs. Or even an unaligned polity!)
Fifth star: Small terrestrial planets, with one icy nebulous panthalassic world. Could be a good place for living in habs as well.
And also a Neptune-like small gas giant that manages to orbit the detached binary and the extra star... maybe. That'd be cutting the "three times" rather closely. But it'd be a fun place for bubblehabs. (Alternatively we could attach it to the detached binary or the fifth star.)
Thoughts?
, serves me right for just checking article titles instead of looking inside. At least I can console myself that I had such a good idea that it's been already used... 