I don't think so. What I hear from nutritionists is "Eat a varied diet". It seems that the needs of the body would vary over time and depend on all sorts of variables in the organism its self and the environment. One of human's greatest strengths and adaptations is that we're omnivorus, that we can eat lots of different types of food. What you're asking about is a monodiet. Koalas and Pandas are the only animals I can think of that have a monodiet.
I agree with norman, (in principle if not in practice due to the somewhat disagreeable idea), surely eating human flesh and/or offal could not fail to provide all necessary nutrients, assuming that the volunteer/victim did not suffer any significant deficiencies? Although I have just thought that apart from the contents of the gut (probably not for eating...) the human body would be totally lacking in fibre, though is this *essential* for living? Or just for a healthy gut?
There are certain vitamins you can only get through eatting animals, and there are certain vitamins that you can only get through eating plants. Therefore, there is no single food stuff that would give you ALL your needed nutrients.There are, however, a number of people in this world that manage to survive without eating meat. IMO they are not getting all the nutrients they need, but they do survive. Thus, I believe it is possible to survive indefinitely on a single food stuff, you would not thrive.