Pretty much the only double rig I use anymore is: larger fly direct to
main tippet, smaller fly on a piece of smaller tippet tied in onto the
eye of the larger fly. I've tried on the bend, tag end of tippet, et
al., but tying into the eye is for me the easiest and least prone to
tangle, and I think is better for hookups on the big fly.

YMMV.

BTW, the larger fly might not be big, on the San Juan I've used #20
and #22 rigs, and maybe even smaller. You can fit two 6x tippets into
a #20 eye. And catch fish on it.

Jon.