Sign up through one form onto multiple sheets at once?

I use various different smartsheets to sign people up for various employee groups (the Smartsheet is a member signup list). Each group has its own Smartsheet and its own signup link.

However, I would like for each signup form to let people choose "sign me up for these other groups"  where they check as many boxes as they like.  This would mean people use the link for one group to sign up but their information would then get logged in for that Smartsheet and for others in my account that represent each other employee group they select to join simultaneously.

Is it possible for people to sign up for multiple Smartsheets at once?