I have several questions on this teaser, hoping this will be considered by the dev team.
First is the Dyson sphere and the ring world. Binary and trinary stars may stop planets from becoming frozen as other stars in the system can still heat them up, while more complicated gravitational relationship may result in building ring world impossible in the system, if theoretically speaking.
Second is some game rule and spawn checking. Dimensional horror, infinity machine and horizon signal event chain require a black hole system to spawn in or trigger. With binary or trinary system it's possible to spawn one black hole and one other star, making the check likely to be stuck.
Last I can come up with is the environmental hazard. Similar to the one above, it's possible to spawn neutron stars, pulsars and black holes in one system. Will their penalty be stacked or the calculation will be changed? If you have two neutron stars in the system while the sublight speed reduction modifier is added (-0.5-0.5=-1 a.k.a. -100%)but not multiplied (0.5*0.5=0.25 a.k.a. -75%), it's possible that all ships entering the system will be literally stopped on the entrance, making them completely unable to move in the system, not to mention building a outpost or surveying the system. (another Dio Brando meme?)
I will post other possible questions and potential problems gathered from my friends later.