I just had an engineered wood floating floor installed in my pier and beam house. The are several small areas where there is a good amount of give in the floor. When you step on the floor it moves up and down about 1/4 of an inch.

The 6' wide engineered planks are glued together at the tongue and grooves. The installer says this should be expected with a floating floor, but the others I have walked on don have squishy spots.

My question is, can I screw down the floor in the squishy areas?

I know engineered floors do expand and contract some, and I'm wondering about potential problems if I screw down a couple of small areas. The radius of the areas is about 10".

Floating floors need to float and shrink and swell with the changes in seasons. Screwing the floor down would remove that ability and you would have buckling or gapping result.

The sub-floor has high and low areas in it, and the floor moves up and down in the low areas because the wood flooring is "bridging" the low areas. Those tongues will eventually break and you will end up with gapping..

1/4" is too much, but fixing it may be worse than learning to live with it. You cannot re-build the house to flattend the sub-floor.
The sub-floor Low areas should have been addressed prior to the installation.

I agree. Improper substrate prep. Installed over an out of spec substrate, flatness specifications were not met.

The floor will eventually come apart because of the flexing.