I think you can use a varient of the method mentioned here
https://community.marketo.com/MarketoArticle?id=kA050000000KzejCAC&refURL=http%3A%2F%2Fcommunity.marketo.com%2FMarketoArticle%3Fid%3DkA050000000LA9FCAW
You can have 2 fields. One field for the 'latest' search string. And the other is the main pipe delimited string of all values.
When the form is submitted, just capture it in the 'latest' value and have a flow action to append that value to the main field using the method described in above link.
Hope this helps
Rajesh