Is it possible to approve multiple items at once?

Yes, within Budgyt, it is possible to approve your team's numbers at the line item level, but also at every level of hierarchy above that.

On the Dashboard, select Approvals from the green drop down menu (this option will only appear if you have Approvals turned on in Settings, and for the budget you are viewing on the Dashboard). This will highlight any categories in which there are items awaiting approval. It will also highlight the group to which that category belongs, and the header. You can click on the Group or Header Names to approve all underlying Categories and Sub-categories for that particular Department. 

Also, if you select a consolidated Region number or Complete Company Consolidation it will approve/reject all unapproved items in all Departments in that Region for the Categories selected.  Clicking on any of the highlighted numbers will display a window where you may leave comments and approve or reject the numbers.