At my company (B747) the following rules for f/o's:
-Rejecting the t/o due to specific failures/warnings is allowed
-No Cat II/III approaches
-After first type conversion 15kts max x-wind during the first year.
(Other types have different rules, B777 f/o's are not allowed to reject the t/o, but are allowed cat II/III approaches, IIRC).