I don't think that such a case exists. The case that might fit the most to your descrition is maybe the Silverstone Grandia GD07.
It can support up to 4 external drives and you might be able to use 8 Expansion cards with a riser card and maybe fit a 240mm radiator in there, but I am not sure.
Otherwise you could buy a tower case and lay it horizontally.

That Silverstone case is a good suggestion. It looks like you maybe able cram a 240 radiator, but lacks airflow into the case. It does have 8 slots, but they're in a 7+1 configuration.

I did consider laying a tower case horizontally, and have done this with some older cases - some look better than others in this format. I was hoping someone would've made something more elegant.

With a riser cable you could still use that 8th slot in the Silverstone case, but the radiator will probably not fit. In this thread http://www.overclock.net/t/1427960/build-log- … ilverstone-gd07, a 240mm radiator was installed outside the case (with the fans inside), but that required to drill two holes. Additionally a 360mm radiator was installed inside, but that one blocked most of the drive cages.

If tower cases are ok, then you could have a look at the the Lian Li PC-10N, which is one of the smaller ones with radiator support and 3 external drives (still bigger than the Grandia GD07, but better airflow).

^^ Thanks for those links - both those cases are interesting. The Silverstone is an art in cramming, whilst the Lian-li is almost perfect if it was rotated for a desktop format. But as you mentioned, it can be layed horizontally to get that look. Both are nice and compact, too.