On our last trip to Italy I noticed that some people were drinking a fresh juice drink that appeared to have blood oranges as a main ingredient. We asked about it and it was called "supreme." We ended up ordering it several more times in other locations, as well. I think it was a combination of several citrus fruits and included plenty of pulp. I was sure that we could come and easily reproduce it - no such luck. Could be our faulty memory, but I would like to see if we could make it. Can't seem to locate it on the web, so maybe my memory of the name could be faulty, as well.

Where are you getting blood oranges?

Perhaps spremuta di arance rosse di Sicilia? Google turns up this imported version (with an annoyingly-designed website): Italian Volcano brand juices.

So that they would not offend delicate American sensibilities, the hotel we stayed at in Venice called them BLOND oranges. For some reason, at 7:30 in the morning, Grover and I found that hilarious.

The drink I am referring to was always freshly made - the hotel where we stayed in Rome served the common juices (orange, grapefruit) as a matter of course, but if you asked the server real nicely, they'd go into the kitchen and would have someone whip up the "supreme." Now I wish that I had followed the server into the kitchen and watched the process.
The drink was also available in cafes (where they'd charge about 6 euros for it).
I don't have any blood oranges now, but I figured I'd do the research now and be prepared when I see them back in the stores (ususally around Nov/Dec I think). I didn't realize that it would be so hard to figure it out.
Thanks for your help!

I think that Trader Joe's sells that brand of blood orange juice.

That TJ's blood orange juice is awful. Think of the worst concentrated OJ you've ever had-- that's about what it tastes like. It's too bad this isn't a good substitute, as getting a decent volume of blood orange juice requires a ton of oranges (due to their thick skin and relative dryness).