Suppose that a $k$-tape read-only Turing machine receives its input on each $k$ tapes. It cannot write on the tapes, but it can move on them in both ways, even move off from the input. So for example, it can simulate counter machines, which implies that it can recognize any recursive language if $k\ge 3$. If $k=1$, then it can be simulated by a two-way DFA, thus can recognize only regular languages. But what happens for $k=2$?
Can two-tape read-only Turing machines recognize any recursive language?