Yes, this is possible. In the example below, after starting with the first survey, midway through we'll link to the second survey. Then, when the second survey is finished, it will link back to the first survey, bringing with it new data.
Let's say the link to the first survey is:
http://www.sawtoothsoftware.com/surveys/pv1/login.html
It is going to use a Start question password called "email" as the unique element between both surveys. I've also selected the "Allow respondents to define their own passwords" checkbox in the Start question's settings tab, which lets the respondent define their own password, disguised as their email address. But you could just as easily give the respondent a pre-assigned password in their "one-click" survey access link.
In our example survey, after the respondent types in their email address, the only thing we are doing in the first part of the survey is to ask the respondent to pick a color from eight radio buttons. The value of their choice is is stored in the "color" question.
After respondents do that, they are linked over to survey 2, using a Terminate/Link question except we don't terminate at all—we simply fill out the link URL with the following link:
http://www.sawtoothsoftware.com/surveys/pv2/cgi-bin/ciwweb.pl?studyname=PassingVariables2&email=[%email%]
Notice that we're using the second survey's "one-click" link because we are sending it the password data (email) — the key to matching up the records. The second survey needs to store the email data we're passing in to it so we can pass it back out when the survey is done. This is accomplished by going to the Start question, Pass-In Fields tab and adding a field name called "email", just like we did on the first survey.
In our example, the objective of survey 2 is to pick out a shape. This is stored in the "shape" question. After the respondent does that we use the Terminate/Link question to set the terminate status and link them back to the first survey. This time, our link looks like this:
http://www.sawtoothsoftware.com/surveys/pv1/cgi-bin/ciwweb.pl?studyname=PassingVariables1&email=[%email%]&shape=[%shape%]&sys_skipto=results
Notice that we're passing back the email variable (so we can re-enter the password-protected Survey 1) as well as the value we collected from the "shape" question. We are also adding a sys_skipto name-value pair that says to skip to the question titled "results". The "results" question simply displays the selected data from the first survey and the second survey.
For more information about the One-Click survey link and the sys_skipto parameter, check out the following item from the SSI Web help section:
https://sawtoothsoftware.com/help/lighthouse-studio/manual/index.html?hid_web_oneclick.html