Well, in both previous games, becoming a vampire did not cure you of any disease you already had. During the 72 hour incubation period, you would be easily capable of catching any other disease, presumably even lycanthropy. And since the transformation to vampire did not cure you (you still had any disease you had when you went to sleep or waited that final time as a vampire), you would still have lycanthropy. Of course as we all know, it was in fact possible to catch diseases in Oblivion as a vampire even though you should not have been able to do so, but that was indeed a bug (not sure if it was the same in Morrowind or not). The same is likely true of lycanthropy in that since it also has the 72 hour incubation period you can cure it to avoid tranforming in, it probably cannot stop you from contracting the vampire disease.
So I see no reason at all why you couldn't nor shouldn't be able to become both without any "cheats" or console at all. It's a normal part of game mechanics working as intended. But what makes it even more likely that you could find yourself as both is the fact that you can become a werewolf without the disease. At least that's the implication of the existance of
in the game. That worked without any need of disease and so was the way essentially that one could become both a werewolf and a vampire in Morrowind. It's use was in no way a bug or exploit (I really cannot understand the insistence on this, since the item was intended to work that way and you circumvented or bypassed NOTHING by using it).
Anyhow, at the risk of angering all the "I sure hope some other people that think this is cool have to svck it cause I don't like it" crowd, I for one hope it is possible and plan to find out soon. To those who might also find it fun, keep them fingers crossed, only a week. Note to lore buffs, the method involving use of an item while already a vampire could be looked at technically as you are NOT both. A "true" lycan does not acquire the form and powers of a werewolf from a daedric item, they had the disease and are restricted by it's state. See what I'm getting at? Technically, vampire puts the ring on, transforms, and is still....a vampire only. Just also has the powers and look of a werewolf. No violation at all.