Tweetbot for Mac can have multiple columns, windows for just about anything you want

Tweetbot Mac columns
Tweetbot, a powerful and stylish Twitter client for the Mac, can open just about any tab or stream in new columns and windows. For example, next to your main timeline you could have a column for your mentions, a column for another account’s mentions, a column for search, a separate window for DMs, and so on.

To cycle focus forward and back between columns, use Tab and Shift-Tab. To close columns, use the gear menu in the lower right of the main column on the left.

You can get Tweetbot for Mac in the Mac App Store.