This is quite difficult to implement. So I have added it to the TODO list, but I doubt I'm going to implement it. Sorry :-(
sorry if this feature was already requested.
my idea is to allow open new sessions while transfer was already started in foreground. there could be button "put in background" in copy window and after pressing it you can browse local directory AND initiate more sessions or navigate through already opened. panel with listing of remote directory where "put in background" is INACTIVE (greyed - no action is possible) until copying is in progress (since we have only one ssh connection)