I don't know what you mean by "simultaneously". Are you suggesting some sort
of ORing of levels, as logger.log( INFO + DEBUG, msg )? That would be
meaningless, since DEBUG < INFO. If a DEBUG message would log, so would an
INFO message.

Are you simply saying you want to issue log statements at different levels
from the same code, as

...
    logger.log( INFO, msgA );
    logger.log( DEBUG, msgB );
?

That is not only possible in log4j, it is a favoured idiom.

However, if your appender is closed you cannot log anything.

<http://logging.apache.org/log4j/docs/manual.html>

- Lew