Currently if a participant purchases a ticket online and then returns at a later date to purchase another ticket, CiviCRM won't allow the same individual to purchase the 2nd ticket under their name. The purchase could register another participant and complete the purchase, but for individuals that want to purchase more than one time under their name, it doesn't seem possible. I am not positive, but I believe this is due to the unsupervised dedupe rule used by CiviEvent. Is there a way to allow the same purchaser to purchase more than one ticket at more than one time under their name online?
In 'manage event' you may be able to check "register multiple participants" and "same email address" if you have a pretty simple event setup. It's a bit clunky but if the same name is used with the default dedupe rule, civiCRM should create another participant for the same contact record. Note that i've only tested this with free events.
The registrant will be forced to go through a page that says "you're already registered, click register to sign up again", by default.
If you need someone to "edit" the same participant record by adding quantity for a paid event, I don't believe that is possible. Doing paid edits to the same participant record is something that even administrators cannot do elegantly at this point (4.6.4 for us) with basically any level of complexity involved, such as changing price sets and/or discount codes.