No, this is not possible. Encoding a message using XOR and a key of equal length, randomly chosen from a uniform distribution, leaves you with a ciphertext that is equally likely as any other possible ciphertext, regardless of what the original message was. Therefore, without knowledge of the key, the encoded message tells us absolutely nothing about its secret.
The security is not compromised by running the algorithm again. It will yield a second number whose probability is also evenly distributed and more importantly, independant of the first ciphertext, as long as the keys are chosen independantly, even if the message is the same. Once again, these two numbers are equally likely as any other possible combination of two ciphertexts, regardless of the original message. So here too, the message stays a secret.
In fact, if this were not the case and multiple versions of the same message, but encoded with different keys, did reveal information, breaking the encryption would be trivial, even with only one ciphertext. An attacker could easily make more, by XOR'ing the ciphertext with another number, as this is equivalent to XOR'ing the message with a different random number.