It is unclear to me what you wish this new button to do. I presume it would take all the values of the Active VIs selection ring and save all their results to the same file. Do you want them concatenated? Or should the timestamps be interleaved into one log file? What kind of correlation do you want between the logs (i.e. one event may trigger many event structures, each of which handles that event at vastly different times)?
Please provide more details about the nature of the aggregated log file that you want to generate.