Be down with means: To be alright, okay, or in agreement with; approve of; stand for; to accept as good, right, or preferred.. It is informal slang, fine in casual speech but not suited to formal contexts. There is no real cause for parental concern; it is descriptive vocabulary rather than risky behaviour. If your teen uses it, context will usually make the intent clear. A short, curious question about where they heard it is usually all that is needed to know whether to follow up.