Here document inside a here document?

Can we use a here document inside a here document?

Something like this

ssh user@remotehost << REMOTE
   sudo vserver vsernamename enter << VSERVER
      perform actions on vserver.
VSERVER
REMOTE

what shell are you using?

Bash!

ssh user@remotehost '
   sudo vserver vsernamename enter << VSERVER
      perform actions on vserver.
VSERVER
'

I tried this. It throws an error saying unexpected end of file.
Error is thrown on line sudo vserver vservername enter ---- unexpected eof.

This syntax works fine with me.
sudo 1.7.0
bash 4.0.28(1)
Sun_SSH_1.5

"VSERVER" the one on the last line:

Must be in column #1 -- ie., all the way left as far as possible.