Some time read up on SSH Multiplexing. The default is MaxSessions 10. You auth once, my phishing exercise can utilize your session to connect anywhere you have connected. Nothing will show up in syslog. I can take care of `lastlog` entries since folks cache sudoer privs for so long; or in some cases, don't even require a pw.
I will set up a github with a working example of how to set up a backdoor leveraging ssh multiplexing. I got the idea from a coworker (whitehat) that used a simple ruby script to completely pwn my system. The cool part is, it doesn't require exploiting anything beyond the helpful developer or sysadmin.