Multiple Search and SUMIF

Hi - I have a spreadsheet (attached) in which I am trying to find the total values in each month, from a yearly total based on three sumif functions - in the sheet these are person, place and category.

I am trying to find a way of searching this criteria and returning the relevant totals per month (a simple pro rata'd across the 12 months is fine)

At the moment I have several sumif formula's but I believe the answer lies in a sumproduct of some variety.

Any help would be very much appreciated.

Thank you!!!