So I have been hearing this construction quite a bit recently but couldnt find it in any of the dictionaries that I commonly use to look up things. So I was wondering just how common it really is and if its only used in very colloquial speech or extends to other areas as well. Then I have also heard "to be down for" but Im guessing this is simply used whenever a noun is needed (to be down for "it", whatever that may be) and is identical in meaning to the other phrase.
From Oxford Dictionaries ( https://en.oxforddictionaries.com/definition/down ):
4.1 On or on to a list, schedule, or record. ‘I'll put you down for the evening shift’
So, "down to do something" means on the list to do something, or scheduled to do something, or otherwise committed to do something.
As for "down with", it's a well known colloquialism. From the same source:
US informal predicative Supporting or going along with someone or something.
‘you got to be down with me’
‘she was totally down for a selfie’
‘‘You going to the movies?’ ‘Yo, I'm down.’’
And from Merriam-Webster ( https://www.merriam-webster.com/dictionary/down ):
5 a slang : cool - a down dude b slang : understanding or supportive of something or someone —usually used with with trying to prove that they were down with hip-hop culture — J. E. White
6 : being on record - you're down for two tickets