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Don't know if you've already figure it out by this point, but using the megastructures icon in the manage tab of the construction ship for some reason doesn't allow you to build more using the core, stating "Cannot build more than one..." (guessing that's what you were using to try and build your second batch using the core). But I found that "ordering" a construction ship to build a megastructure (commanding a construction ship and selecting an uninhabited planet, star, etc, in a system with no megs) allows you to build your second batch. Also I'm pretty sure the build meg menu has been bugged for a while now with the Art Installation still being "available to build" even though you already have one built, with or without the core. Hope this makes sense and helps!