Thanks for posting it here. It would be great if you can elaborate on the intention of asking for this feature. There are a couple of ways I can suggest now, let me know if either of them solves your case.
1. If the intention is to avoid notifications for certain time period, you can use the Alerting period and Don't alert me option under the Admin > user management > users > Alert settings
Alerting period when set would alert you through SMS/Voice only during the set time and Don't alert me will not alert you for the selected day. Below is a configuration I have made where I have set my alerting period as 8 am till 8 pm and set Sunday as my alert free day ;).
2. The other alternative I would suggest is to ask your team to install our Site24x7 mobile app (iOS, Android) to get notified on the alerts. This way, each individual in the team can have control of the notification he/she receives.
You can then configure sms for important teams like the operation team. This will enable important members in the team are notified always and others may choose in the mobile app to receive notifications or not (You would still get notifications for all configured monitors in the app but can turn off notifications).
Product Manager, Site24x7