Big Mail supports multiple email accounts, as well as sending from different aliases.
You can create new accounts by going to the Big Mail app:
An alias must first be configured with your mail provider. For example, on Gmail it must first be added via the web interface.
Once configured with your mail provider, select the account in Big Mail and choose “Manage Aliases”. Then you can enter the from name, and from address.
Aliases will then appear in the compose window.