You can prune it ,down to three to five trunks,but if you live in cold climate ,the pruning has to be done in the Spring not now,so you start pruning the dead trunks first.
I see you live in AZ,but ,havy frost in the desert is possible,so Spring is the time of pruning.
When tree has ,100 trunks it defend itself from cold ,by providing shelter to itself,and braking the cold wind.
Some trunks die some live,but ,if left alone now it will have some live trunks in Spring,and then you choose what to keep.