For new Q&A sites, does Stack Exchange offer their framework so that other teams can create new sites or is it all in-house?
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Area51 is where new sites (topics, as you put it) can be suggested.
There is a whole process of them going into private beta, public beta and graduating (or not).
The process is public and community driven - anyone can suggest a new site, so in many ways - nothing is "in-house" (very few exceptions - the original trilogy of Stack Overflow, Super User and Server Fault and Ask Patents, which was a special deal with the US office of patents).
If you are talking about making your own site outside the Stack Exchange network...
Then yes, you are allowed as long as you:
I think I covered everything, but comment if I didn't.
You can't copyright the look and feel of a site or app. You can patent it, but as far as I know, SE doesn't have any patents (again, comment if I'm wrong).
If you are talking about making another site inside of the Stack Exchange network...
Then yes, you are still allowed :-).