Using all of those cores

Parallelism for a code for a specific problem?: You have to find a more parallel algorithm. If that is even possible.

Making efficient use of compute resources, in a world where the codes you want to run have limited parallelism? Run many different codes together on the same compute elements, and switch between them to keep memory bandwidth and compute occupied. No single code will run faster, but at least you maintain throughput in the aggregate.

This is kind of where computers have gone anyway. From your phone, to your desktop, to servers running containers running jobs in the cloud - they've all got many many dozens of jobs to run at any given time. If one stalls, switch to another.