Table partitioning based on multiple criterias possible?

New to Pg and wondering the extent of PG's table partitioning
capability.

I have a huge table > 18 million rows(growth rate ~8 million a week)
which I like to implement partitioning.

Initially the plan is to just partition it by date. eg: 1 partition per
month.

Now, I'm thinking if it's possible to also partition them by
product/items.

is it possible to do multilevel partitioning sort of like

if month = July then go to July Parition
if Product = Shampoo then go to shampoo partition
elif Product = Soap then go to soap partition

something like that..

Thanks