I assume just putting them all together and distributing as a single undifferentiated thing would be a big no-no under the GPL.
Is it acceptable to hive off the GPL assets and say those are subject to the GPL and everything else is subject to another licence?
EDIT: Guess not.
However, in many cases you can distribute the GPL-covered software alongside your proprietary system. To do this validly, you must make sure that the free and nonfree programs communicate at arms length, that they are not combined in a way that would make them effectively a single program.