Hi @doyouhappentoma,
Hope you are doing well. Thanks for reaching out!
The settings you are looking for are available under the Shared Notifications settings in your account.
More info about it here: https://adobe.ly/46bqdUR
Hope this helps.
Unfortunately, S.S., you suggestion isn't the answer. Recipents don't typically have accounts that are shared with me which is the trigger for these notifications you suggest. "Shared Notifications is a separate set of email and event triggers for the agreements of users that have shared their accounts with you." It really isn't even clear how or why someone would share their account with someone and because my recipents don't "share" their accounts with me, I can't control the notifications. Additionally, for someone else to control their own notifications, they must have an Adobe Sign lisense which most people don't have.
While I was testing and racking my brain trying to come up with a soluation to this notification problem, I did figure out that creating Custom Workflows in Adobe Sign can add a layer for recipent notification choices. I can't explain the different between sending a template through the "use template" option or the "custom workflow" option but when I "used template" I couldn't change recipent notifications and when I used a "custom workflow" I built with the same template, I had options to not send recieipents notifications. It is mostly what I needed but definitely still has issues (it is marked to send the sender [me] an email when it is all signed but it doesn't).
Anyway, workflow helped with the issue. I don't know why the built in "use template" system is so terrible and limited in its notification options.
https://helpx.adobe.com/sign/using/video/how-to-create-an-easy-to-follow-send-experience-in-adobe-sign-using-workflows.html