For phillips head screws:

Use a well-fitting, sharp edged screwdriver. There is a lot of variation in no. 2 screwdrivers the way they fit in the screw head, for example.

Use a drop of valve lapping compound in the screw head for a little extra grip.

TIGHTEN the screw slightly to break it loose before loosening. If the screw had been previously damaged during removal, you will be more likely to break it loose.

If all else fails, these are handy when used with a rivet gun:
https://www.ustool.com/store/cart.php?m=product_detail&p=1531 . It hammers the screw while you turn the wrench handle. It works similar to a hand hammer driver, but more controllable.

Dave Evans
52_3100