This app was mentioned in 7 comments, with an average of 1.14 upvotes
MailDroid / MailDroid Pro.
Link to pro-version: https://play.google.com/store/apps/details?id=com.maildroid.pro
I recently started using MailDroid and I could not be happier. I think it covers your use case.
I'm use MailDroid https://play.google.com/store/apps/details?id=com.maildroid.pro
Did you check out MailDroid Pro? It's the most complete mail app you can find.
https://play.google.com/store/apps/details?id=com.maildroid.pro