Platform upgrade first. Always.

Yes. You should prioritize a platform upgrade over adding more DDR3 RAM.

16GB of DDR3 is still usable for most things—browsing, office work, even moderate gaming. Going to 32GB on that same old platform means spending money on a dead end. That cash is better saved for a new CPU, motherboard, and DDR4 or DDR5 RAM. The performance jump from a newer platform will dwarf any benefit from extra RAM on an old one.

Unless you have a very specific workload that absolutely needs 32GB right now (like heavy video editing or multiple VMs) and can’t afford a full upgrade, don’t bother. You’re better off putting that $50–80 toward a modern system that will actually feel faster.

Future You will thank you for not throwing good money after obsolete hardware.