You could try Airmail. The beta version is free to download and fully usable. So you don't have to purchase it in the App Store and may test it before that. I'm not sure if it has a calendar or a plugin for it, because it is installed on my other MacBook at home and I had no need for a calendar.
It has integrated very much online storage services like Dropbox and OneDrive for saving attachments I think and also syncs accounts over iCloud.
I like it very much. Works with all accounts I tried (iCloud, Gmail, GMX, AOL, Outlook and some unpopular others).
There will also be an iOS version soon, that can sync your accounts from the Mac application. I have a free beta of that too, but you can't register for it anymore and have to wait a little.
http://airmailapp.com
Just click on Beta and download the new version from yesterday.
Edit: I tried several e-mail clients before, because Apple Mail just has too much issues with my main e-mail provider, if I have more than one account there. Found nothing better.
Postbox seems also to be very good at all. It has a trial version and even if you buy it you can get your money back within 60 days or so. I can't remember why I cancelled the purchase, but I got my money back very fast.
https://www.postbox-inc.com
I might remember it is able to use Thunderbird extensions.