FTP connector has post command
I can confirm the ftp/sftp connectors do not support arbitrary calls after the PUT. I had another client with this need and their solution was to develop their own ftp connector using the connector sdk to get the functionality specific to their use case. Not super diffficult if you have Java expertise but not a trivial effort either.
I think your situation sounds similar to Allow FTP "site" commands before/after putting file. I encourage you to vote for that idea.
Retrieving data ...