Norton Family - Enable dynamic requests and responses for additional screen time

Microsoft Family Safety in Windows 8+ does this best.  When time is up on a particular device, you should offer the option to request more via SMS, e-mail, or (preferably) Android mobile app notification, and for the parent to grant a variable amount of additional time (whether time allotment per day or extension of allowed hours).  It's a huge pain to temporarily adjust the allowed hours (and then remember to change them back) under time supervision for one-time exceptions to house rules.