I have several Gmail accounts, 3 personal,1 university account, a yahoo account and an iCloud email account. In trying to trace poor battery life issues with my iPhone 5S, I'm tracking down battery hogs and fetching with 4 gmail accounts is supposedly a big one. I really like the built-in email client and would like to continue using it. I suspect there may be an app or service that can send push notifications for my gmail accounts to my phone, telling me to open the built-in email client and then let it fetch the message. I don't know of any such app but surely one exists. If the gmail app can do push, there is clearly a way someone else can too. Failing that, I wonder if I could set my synology NAS to handle my emails for me, including push notifications.