No one seems to know - not even the man who came up with the script. When asked in an interview what the plot was, Sam Hall said that he couldn't remember anything about it. And if the plot was actually such that he couldn't even remember it, perhaps it's a blessing that it was never made...
Howdy! Actually, I may be able to put this urban myth to rest for good... I've discussed this with both Sam Hall and Dan Curtis previously and there was never any script nor an outline written for a proposed Barnabas-centered sequel film. When I asked Hall about it, he couldn't recall how much thought they'd given it, and his only impression was that Curtis wanted to make sure there was a role for Kate Jackson in it, because he was impressed by her. Curtis said that they put in the bat gag at the end credits, but never had thought beyond it. As he described it, MGM called him, delighted with how HODS was doing at the boxoffice and said they wanted another one. He went and had a lunch or dinner with Frid to tell him about it, and Frid said he wouldn't do it. That lunch is where the oft quoted exchange below is supposed to have happened:
Frid, "Friends have all warned me about continuing to play Barnabas-- I'm concerned for my image."
Curtis, "What about the image of an out-of-work actor? How about that image?"
I pushed on the point again with Curtis, "Not a rough outline, a treatment, nothing?"
Curtis, "No! We never got there. MGM said they wanted another one. I asked Frid. He refused. That was it. Period."
There have been rumors about this for years, but I think it's just a game of telephone, a rumor or comment stated by people back in the day, that has bounced around ever since.
Oh, I wish there had been though!
There is a story breakdown/treatment for NODS with some solid differences, but nothing with old Barny.