@Z-tight

Thank you for your response.

Let me clarify.
1. I signed the unsigned transaction with wallet A and it said partially signed. I didn't save the partially signed transaction.
2. I repeated this for wallet B, so I signed the unsigned transaction again (so not the partially signed transaction of wallet A, because that one I did not save.) and it said again that is was partially signed. Again, I didn't save the partially signed transaction.
3. I repeated it again for wallet C. I signed the unsigned transaction and it said (full) signed! It was not necessary to sign it with another wallet in order to broadcast it.

I thought, this is not possible, but I repeated this process 2 times again to verify.

Hope it's clear now.