Hello there. I have an older house with an older plumbing system for starters. It is a three handle shower/tub unit. The cold water value leaks through the value stem when turned and leaks even more when the diverter is turned to the shower head. We have had 4 plumbers try to fix it, but the leak continues and what is worse, the water leaks downstairs and has caused cracking and water damage in the ceiling and walls. Any advice would be welcomed. Thank you.

If tightening the packing nut won't stop the leak remove the stem by putting you wrench on the shoulders of the stem. Either replace the packing gasket material or replace the stem. Four plumbers huh.
You will probably need a tub facuet wrench to to this.