This is a cool pattern! I drew it up in EQ to play a bit.
I would stick with 6 inch blocks and just make more. If you increase it to 12x12 blocks (72"x72"), it would look like this:
I like seeing more of the chain pattern. You could then add borders to bring it to the size you want.
Once I drew it out, I wanted to close up the loops. I added another round of background squares and paper pieced blocks, like this:
That appeals to me, but the finishing blocks are a bit too pointy. I modified them a bit, and got this:
This layout is 84"x84", so would make a good queen quilt by adding 6-12 inches of borders (total).