Yep, that's no problem. A server isn't actually ever an ssh client, it just might happen to run one as a particular user
sshd is the 'remote ssh host' and runs as root, then splits of a version of itself for each user connecting, this split off version runs as the connecting user and looks at $HOME/.ssh/ (on the 'server' side) for keys etc.
ssh is the 'client SSH host' and runs as you, it also looks in $HOME/.ssh/ (on the 'client' side).
If you want a hand laying out what keys need to go where, let us know the usernames you are using and which server they are on (or call them 'user1' etc).