Is there a way to...

[Fyron]

Even in SE3, you could still only have one SY working on a ship at a time. Ships/bases just had the ability to have multiple SYs, each with their own build "queues."

SY Expansions direct link.

[Suicide Junkie]

The UI to link such yards together would not be fun to use...

In any case, though, what is wrong with building batches of 20 warships every 5 turns instead of 4 warships every turn?
And if you stagger your queue completion times, you get 4 warships every turn from your stack of 20 BSYs already.

[Urendi Maleldil]

Actually, you can mod an AI script to create a design with more than one space yard component for you and both yards will contribute their build ability to the same construction project.