Can I transfer files between two remote servers with WinSCP

SFTP protocol does not allow this.

With SCP protocol it may be theoretically possible. However it has many drawbacks. It would require not only major changes in WinSCP, but also many extensive configuration changes on both servers to allow authenticate on the second server from the first one (note that it would not be possible to use password authentication). So practically it would not have any advantage for most users.

For FTP protocol has an FXP extension that allows this, but it is not supported by WinSCP.

WinSCP does not support this well, but you may open two WinSCP instances, connect to each of the servers and then use drag&drop between them. You must disable the drag&drop shell extension first. Files will be transfered through your local computer, using your workstation’s temporary folder.