To increase the size of a mailbox in Plesk, please do the following:
1. Log into Plesk
2. Click on the domain you'd like to modify from the domains list.
3. Click on the "General" tab
4. Click on the "Customize" button
5. Adjust the value of "Mailbox size" to a value you'd like. (Please not this will change the default mailbox size that is allowed for all mail accounts for this domain)
6. Click on "OK"
The default mailbox size has now been increase for this domain.