The crib-drag attack applies with a different operator.
p1 = AtextencryptedByFirstPassword
p = HelloHelloHelloHelloHelloHell
c1 = ciphertext1ciphertext1ciphert
p2 = ASecondEncryptedTextBySecondPassword
p = HelloHelloHelloHelloHelloHelloHelloH
c2 = ciphertext2ciphertext2ciphertext2
When you $c_1 - c_2 \bmod 26$ you will have the same problem as many-time-pad. But this time instead of $\oplus$ we will have plus modulo 26.