Audio editing for drowned out voice

Couldn't tell you without hearing a sample, but the chances of success aren't very high at all. If something louder in the same band comes along, you can't remove it without removing the quieter sounds as well - as dictated by the laws of physics. The only software that can get around this in part does so by analysing the harmonic content of what's there and attempting to separate the speech harmonics from the music harmonics. This is a specialised job, and not something that Audition can do. Not only that, but at best you can hear the words afterwards, if you're lucky, but it really won't sound good. iZotope's RX software can make an attempt at it, but it's not that cheap, as you need the advanced version - over $1000, although I think there may be a short-term rental deal available.