You can only have one SHIP YARD per base. Any more, and they will not work. HOWEVER, you can have more than ONE base.
On my home systems, I build two Shipyard Bases per planet. That way, I can churn out 3 ships per planet every few turns if need be. Hope this helps.
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Creator of the Star Trek Mod - AST Mod - 78 Ship Sets - Conquest Mod - Atrocities Star Wars Mod - Galaxy Reborn Mod - and Subterfuge Mod.