Rehashing PBKDF2 hashes - do iterations stack?
PBKDF2 consists of a chain of one way functions. The one way functions are dependent on each others output and this output is computationally unique. That means that there are no shortcuts of creating a specific outcome.

So yes, you can chain the PBKDF2 functions that way. However, it won't be binary compatible with just using PBKDF2(20, password) as the concatenation of the steps that make up PBKDF2 will be different for both, even if you re-use the same salt.

Reusing the salt won't lead to problems, as the output of the previous PBKDF2 is randomized, so it will be different from any other password / output of the first stage.



Notes:


PBKDF2 directly uses the number of iterations, i.e. the work factor will increase linearly. Unfortunately computer processing power doesn't, it seems to continue to increase faster than that.
It may be a good idea to store some kind of version number with the PBKDF-2 hash so it is possible to distinguish between different forms of hashing (such as single PBKDF2 or extended PBKDF2 use as described.
TL;DR, option 2 is correct - yes iterations do stack.