This function is available in Skylight.
The second version can be approximated by "survey to make a survey"
http://wsuctlt.wordpress.com/2008/09/26/survey-to-make-a-survey/ but
not on the fly. The respondent would complete one survey and then
later be asked to complete a second one.
If you know metadata about respondents, eg, year in school, major,
etc, then you might consider a matrix survey. Start by creating
multiple respondent pools, one for each group. Author questions in
question groups with the different groups of questions keyed to
different respondent pools. All groups can get some common questions,
see this example
http://skylightkb.wsu.edu/getting_started/what-is-a-matrix-survey
For completeness, there is a third name for this kind of survey,
"conditional." Conditional designs place some logic on each question
and can use data the respondent has answered and/or metadata available
to the survey engine to show/hide the question. These can (in
principle) be quite complex conditions, such as if
[respondent.gender=male] AND [respondent.age>25] THEN ...
On Nov 3, 1:16 pm, meredith conover williams