The shipbuilding rules doesn't seem to make clear whether one can take multiple bridges. Can you?

I wouldn't see why not, alot of naval ships today have an auxilary bridge.

I'd say no; the SP costs for them assume you're only buying one.

No, it specifically says that you can only have one of each essential component.

But like with anything else if the gM decides otherwise....

I quite like the idea of purchasing multiple versions of components, including essential components. While some such as warp drives and gellar fields would have no effect (beyond providing redundancy and hence making it more likely a ship will not be stranded by battle damage), i can definately see the benefit of a small ship having 2 plasma reactors, 2 bridges, etc.

Imagine the situations.

A cruiser loaded with a second plasma drive and equipped with multiple lance batteries. Sure its gonna be badass, but it'll lose so much space that it would only be useful as a specialist vessel, perhaps one built for fleet support or planetary bombardment.

As mentioned by Thaddius modern naval vessels often have a backup bridge. I wouldn't allow benefits to stack as you could only use one bridge at a time, but if you lost one bridge, the ship could still be commanded via the new bridge.

I also like the idea of multiple non-essential components. For instance, in spacefleet there was a galaxy class troop ship. How about a very lightly armed frigate with the barracks component purchased 4 or 5 times. Bingo, troop ship.

Want an ironclad. Get a cruiser and load it down with 5 armour increases, plasma battery for the prow gun and munitorium and you are set.

The ship design system is very flexible like this. I rather like it.