[Dovecot] courier-imap and dovecot in migration process

Hello! I plan a migration from courier-imap to dovecot. at now run courier-imap as imaps server only and with perdition as redirector. can i run courier-imap and dovecot at same time on the same server(listing on diferent ports of course), i mean with shared home directory tree (Mailbox dir) ?

Maybe access conflict or some problems ? Thanks a lot