Two transactions are signed by different private keys, and the value of "R" for these two transactions is the same?
Assuming the two private keys are unrelated, the answer is no.

The reason for this is simple: there are 3 unknowns (the two private keys, and the single secret k value), but only two equations (the ECDSA validation equation for both signatures).

If a relation is known between the two private keys (like one is twice the other, or one is one higher than the other, ..), another equation becomes known, and the system becomes solvable.