Matt,
I'd check out some of my slides on these:
http://www.marketingrockstargudies.com and look for "engagement"
The beauty of the Engagement is you can add new people any time, but each new lead starts at the top of the Stream. All you need to do is run the entry campaign again (or a new one) and say "Add to Engagement, Stream 1" The cast only deals with leads already in the system.The new group wouldn't receive the first email until the next Cast.
Now if you meant that you wanted each new group to receive the first email now, and then wait 3 weeks, then I believe you need to have a separate stream or Program.