I use CASE almost exclusively. IF would be when there are two choices, CASE when more. But you can use CASE instead of IF. The great thing about CASE is no nesting is needed.
You could also do what you want with a SubSummary part for Branches under the Company SubSummary.
But if I use Case, do I need to create specific combos of the criteria? Project = "apple" vendor = "orange" ; result is total per location spend.
Is there no way to create a calculation that doesn't rely on specific terms?
If you are generically wanting totals by Company by Project by Branch; no CASE statement is needed to do that. You would have SubSummary parts on the layout for the subtotals you want. If you did want a report only on Project = ORANGE, then FIND those records first. Then do the sort and view/print the layout.
WIthout a more detailed description of how you are recording the data --your fields, relationships, tables... are suggestions can easily assume things very different from what you have.
Here's a tutorial on summary reports (Which is what TKnTexas is describing) that might be helpful: Creating Filemaker Pro summary reports--Tutorial