When you need multiple twitter account then you have to sign up with new email address, which will be difficult for signing in and takes too much time.
But …..
I have found a trick to sign Up “Multiple Twitter Accounts With One Email Address”
[Note :This trick works with only Gmail or Google apps addresses. Other email addresses like Yahoo, Hotmail, Outlook won’t work. ]
You can use those aliases to sign-up with multiple Twitter accounts. Twitter will treat username@gmail.com. user.name@gmail.com and use.rname@gmail.com as different email addresses. Though Twitter treats them as different, they are just the aliases of the same email address and they will point the same Gmail inbox. All the notification emails from your different Twitter accounts will reach the same inbox. Thus you can deal with multiple Twitter accounts using a single email address.
If you use Google apps address, you will have to activate the catch-all option in your domain settings. So, it is better that you use a simple Gmail address to avoid complexity.
Alternative trick
When you sign-up for a Gmail account, it automatically create another valid email address with the domain googlemail.com. For instance, if your Gmail address is yourusername@gmail.com then it automatically validates yourusername@googlemail.com. So, if your concern is to deal with only two Twitter accounts, you can use this trick.