Twitter now supports multiple accounts on web
Robert Wallis
If you manage multiple accounts, but like Twitter's native web App, good news. You can now manage up to five accounts in one web browser.
Here's how to add another account
Click more ...
Click the +sign in the top right of the nav' panel.
Click add an existing account.
Add the accounts username and password.
Login
Click More in the side nav' when you want to switch accounts.
Switching between accounts in other areas, like posting composer, is not currently supported. Hopefully that will come later.