any merit in studying two different styles of karate?

Yup there are a few fists like the one mentioned, sanshitanken iirc, also ipponken ( extended first knuckle fist) but you wouldn't pick one and say 'this is goju fist any more that if you happened to walk by the dojo and see shuto being practiced 'oh goju ryu don't use fists they use a chop'.
They are tools in a tool box, you dont use a hammer to install a screw...........(whistle)

 

To the op, much better to spend twice the time on one than splitting it in this way. It makes more sense to train a striking art with a throwing art (for example).
Goju and Shotokan have no Kata in common, certainly up to Shodan level, and even after that any common kata will be executed from very different perspectives and with different strategies in mind.
Better to have a single, deep, core art supplemented with some cross training than a confused mix of superficially similar, strategically incompatible striking arts.
Why be average at both when you could be good at one?

 

I would at least if you were going to do Karate try and find one that was considerably different. Like Isshin-Ryu.

 

Just my opinion, but you should reach a dan rank in one style before starting another. Once you've hit that level, your understanding is on a level where you won't screw yourself up by mixing styles.

 

Thanks for the krotty info, all. Very interesting.

 

Who would? That's not what kata is for.

"Well Officer, I dropped him with the first technique, but I couldn't run away immediately as I had to stay and finish my kata"