It is common knowledge that a universal Turing machine can simulate any Turing machine with logarithmic overhead. Is it possible to make this overhead constant by constructing an analogous "Universal" multi head Turing machine?
If we have a fixed number of tapes then yes we can simulate them without the logarithmic overhead. E.g simulation of two-tape (and in general $k$-tape) TMs on a two-tape machine can be done without the logarithmic factor increase.
If we want to simulate an arbitrary constant number of tapes then AFAIK we don't know any such simulation.
See these questions and the references there: