The easiest thing to do would be to make another table to store the "attachments" with the following fields:
ID, e-mail ID (FK), attachment
I realize that your situation not actually be e-mails and attachments, but I wanted to keep the same example to make things easier.
After you need to make an e-mail form to record data about the e-mail. On the e-mail form, you need an attachment sub-form, which lists all the attachments for that e-mail. You can format the attachment sub-form so that it only shows one record at first, so you can add an attachment, but after an attachment is added, another "attachment" combo box is displayed for an additional attachment. As you continue to add "attachments" and they take up more room, scroll bars will automatically appear on the subform so you can scroll through the attachments.
I know you mentioned adding fields to the table, but I think having a seperate table to store attachments would be more appropriate since, when you have multiple attachments, the database is still normalized.
Let me know if you need any more help.