Hello there, @jessica54. 

Yes, multiple classes could be set up for a single employee. The Class tracking feature is really useful for the situation you have. 

We can categorize the works of an employee into different classes in one day like what you've described. We'll just need to enable the settings to assign classes per item because that's where we assign classes to when creating paychecks. 

You can use the same earning item per division or you can create different earning items per division as well. This will also apply to billable jobs performed by employees.

First, we'll enable the settings to associate class to earning items and jobs:

1. From the Edit menu, choose Preferences.
2. Select Payroll & Employees and click the Company Preferences tab.
3. Put a checkmark in the Job Costing, Class, and Item tracking for the paycheck expenses checkbox.
4. Select As one class per Earnings item.
5. Click OK to save your changes.

Second, create a paycheck for the employee. Your payroll detail would look like this one. 

When you need to know your expenses per class, just go to Reports, choose Company & Financials, then Profit & Loss by Class. 

Also, for future reference, you can check this article to learn more about tracking payroll expenses by class, department, or location.

You can also have this article handy to know more about customizing reports in QBDT: Understand reports.

Let me know if you have any other QuickBooks or payroll questions, I'll always be here to help you.