Having multiple Twitter accounts with the same email address is possible only if you use a Gmail account.
The reason for this is that Gmail does not take into consideration dots (.) in an email address. You can add a dot anywhere in the username and all emails to that new alias will reach your mailbox.
For example, if you use 'example@gmail.com' as your usual email address, you can also use:
'ex.ample@gmail.com', 'examp.le@gmail.com'
or any other combination where dots (.) are used in the original email address.
Therefore, the first Twitter account may be set up with the email address 'example@gmail.com', your second Twitter account could be set up with 'e.xample@gmail.com' etc.
There is also a second way that you can use this system:
When setting up your first Twitter account, you can do this with your usual email address - e.g. johnsmith@gmail.com.
Then for the second, you can write johnsmith+1@gmail.com, then johnsmith+2@gmail.com.
All of the email notifications you receive will go directly to your original email address: johnsmith@gmail.com.