Multiple Appenders with single DailyRolling log file

My goal is to have a single DailyRolling log file but I would like to have a
different conversion pattern for a subpackage.  My current config resembles
the below.  This works but not surprisingly, the file doesn't roll over
because the second appender prevents it from rolling.  Is there another way
to do this?

log4j.logger.my.package=INFO,appender1
log4j.logger.my.package.subpackage=INFO,appender2
log4j.additivity.my.package.subpackage=false

log4j.appender.appender1=org.apache.log4j.DailyRollingFileAppender
log4j.appender.appender1.File=${log.dir}/mylog.log
log4j.appender.appender1.DatePattern='.'yyyy-MM-dd
log4j.appender.appender1.layout=org.apache.log4j.PatternLayout
log4j.appender.appender1.layout.ConversionPattern=%d{HH:mm:ss MMM dd} %-5p -
%m%n

log4j.appender.appender2=org.apache.log4j.FileAppender
log4j.appender.appender2.File=${log.dir}/mylog.log
log4j.appender.appender2.DatePattern='.'yyyy-MM-dd
log4j.appender.appender2.layout=org.apache.log4j.PatternLayout
log4j.appender.appender2.layout.ConversionPattern=<<APPENDER2>>%d{HH:mm:ss
MMM dd} %-5p - %m%n

Thanks.

Chrissy.
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