You can if the partition uses new storage rather than swapping in-place (which is likely what you want anyway for horizontal parallelism, see below): pick multiple pivots and insert elements into a bucket depending on how many pivots they're greater than. This turns out to be called samplesort, with some extra detail regarding picking the buckets.

However, once you give up on in-place you should probably use radix sort instead, as long as your elements, or their hashes, have some semblance of uniform distribution: this avoids having to calculate greater-than on a large number of pivots, although depending on the architecture it may be possible to do the latter reasonably quickly, and I suppose you may end up saturating memory bandwidth anyway...

Anyway, you can run a single partition in parallel - just not in place - by dividing the input data and having separate output queues per core. You probably need to merge the buckets back into the original array anyway, so this doesn't hurt; even if you want to keep the buckets separated (but individually contiguous) for some reason, e.g. if you don't need the final output as an array and want to save some difficult-to-parallelize merging, it just makes the partition a bit trickier with some atomic stuff.