Can my CPU handle 32GB of RAM?

Yes, unless your CPU is from 2012 or earlier. Modern CPUs (Intel 6th gen and newer, AMD Ryzen 1000 series and newer) support at least 32GB, with memory controllers built for 64GB or more. The real bottleneck is your motherboard—check its QVL for 32GB kits, but any standard 2x16GB DDR4 or DDR5 kit works in 99% of boards from the last five years.