I deal with a lot of double sums / double products. I would like to be able to massage TeX into producing something like this:
(that was made with the gimp) ... and a product in product symbol as well.
You can have a look at the section Joining and overlapping existing symbols in manual of Comprehensive Symbol List.
For what it is worth, Unicode defines
If you are able to use
STIX/XITS Math gives and Cambria Math gives .