In addition to customizing the content/display of the Timesheet with Custom Settings, you can also add custom fields.

Step 1: Add Field to T&E Item

In Setup > Create > Objects locate T&E Item and add a new custom Field. Note that it should be editable (i.e. not a Formula).

Step 2: Add Field to Field Sets

Tn the Custom Object T&E Entry, locate the Field Sets section.

Edit the Entry_Timesheet entry: Drag the Field(s) you want to add to the In the Field Set section.

Step 3: Include them in the Timesheet

In Setup > Develop > Custom Settings - click on Manage Accorto Settings

Click Edit and locate the T&E Timesheet Fieldset entry and enter a heading. If you have a single field, that would be just the name of that field. For multiple fields, enter the headings separated by / or |.