Add Multiple SUMIFS Into A Single Cell / Function?

In a workbook I have a tab with multiple columns containing names, activity codes, billed hours, etc. On another tab I have created a budget for which I use the Excel SUMIFS function to check the database in the first tab for relevant entries and add them together in the budget sheet.

Now here's for the tricky part. On the budget sheet the names are not mentioned, only the job titles. So these are grouped together. This means that the first tab shows only names, while the budget tab only shows the function title.

The function I have used thus far is this:

Formula: [Code] ......

The first part refers to the column containing the billed hours, the second part refers to the column containing the names (criteria range 1), the third part refers to a specific name (criteria 1), the fourth part refers to the column containing the activity codes (criteria range 2), while the fifth part refers to a specific activity code (criteria 2).

This works really well as long as the budget tab only mentions the names, yet it only aggegates at the job title level. Would it be possible to use the same SUMIFS function to search the database for, say, all the names that fall within one specific job title? Essentially that would result in this somewhat bulky function:

Formula: [Code] .....

Clearly, Excel doesn't allow this.