That's unfortunately not possible at this moment. We're able to modify everything about the Synthetic check including settings and deleting separate clicks but not actually add one.
The team is continuously improving and extending Synthetic. If this is a feature that you would be really interested in and have a valid use-case - feel free to post a RFE on the Dynatrace Product Ideas forum.
Edit: looks like the RFE has been accepted by R&D.