LogFAQs > #953424445

Theoretically they were building more than one at once. The first Death Star was seen under construction at the end of Episode 3. It was only made fully operational during the events of Episode 4 (or I guess Rogue One now but either way) that means it took 18 years to complete. Thus the second Death Star must have been under construction long before Episode 4 since Episode 6 was only 3 years later and there's no way they completed over 50% of the structure, as well as fully operational weapons systems, in only 3 years when the first took 18 total, especially since the second was bigger.

Also given that it takes 18 years to fully complete a Death Star, it's unlikely that building more than two or three at a time is feasible.