I'm self-employed and use a Windows laptop (Lenovo), iPad and Nexus 6.

I have two email addresses, one that I mostly use for personal emails (Yahoo) and one that I mostly use for work emails (Gmail). I also own a domain, but rarely use that email address, though I do have one.

I have two clients that white label my services and have given me email addresses on their domain. In both cases, they're using Outlook web clients, but they're different interfaces. One is Outlook Web Access on exghost.com, while the other is Office 365 on microsoftonline.com.

Regularly checking four email addresses is a headache, particularly since the two client email addresses log me out frequently and may not have any activity for days at a time. I currently have both set up to forward all incoming messages to my Gmail account, so I know when there's something that requires my attention. (I don't reply from Gmail, rather log in and reply from the proper email address.) Currently, I only access the two client email accounts from my laptop.

On my Nexus and iPad, I use the Gmail and Yahoo-specific mail apps, rather than the generic email app. But I feel as if I should consolidate, since I can't currently log in to read/reply to messages that come into my client account when I'm on my phone or iPad. (Technically I could go to the browser and log in that way, but it's a headache.)

Any suggestions for an Android app that will:
* Allow me to consolidate all four accounts into a single app
* Defaults to the proper email address when replying to messages
* Allows me to have separate signatures tied to each email address

As a big bonus, it would be a tremendous help if the app allowed all to be directly tied to my Google calendar. Currently if I accept a meeting invite on my client email addresses, it dumps the appointment into separate Outlook calendars that I never look at.