If the Übermensch were bioengineered from scratch he/she would necessarily be immune to viruses, at least for a few generations. A normal immune system would confer no greater protection to bacteria and fungi than humans already have, though he/she may perhaps be engineered to produce toxins and antibiotics in his/her blood, though again this would not last. A more long-term solution might be to engineer entirely novel bionanotech immune cells/molecules which natural pathogens have never encountered.