More than one Singularity Power Plant
https://www.dropbox.com/s/9okmvv7oxmor9br/GC3_Two_Singularity_Power_Plants.jpg?dl=0
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In my current game I managed to build two Singularity Power Plants (see external link). When I rmember correctly I was able to build the second one while the first one wasn't finished yet (it still appeared in the list of buildable structures). Only when one Plant was ready one one planet it was removed from the buildable structures list of all planets.