Too much competition at branch origin in mature Japanese zelkova

[curiousAboutTrees]

I don't know how old this tree is. I can go 14 years back on google map and this tree is at least 14 years old. As you can see, lots of main branches originated from the same area and it seems like there is too much competition.

Should I take one branch out every few months or leave them the way they are?

Here is a picture of the whole tree.

 

[Raintree]

This tree doesn't appear to be in the best of health. Don't prune off healthy limbs for they are energy producing.