One issue with most hash algorithms like SHA-256 is that it is inherently serial. You can't effectively use SIMD to parallelize a single SHA-256 calculation.
However, you can calculate multiple SHA-256 hashes in parallel efficiently, because you can keep each algorithm in a lane of the SIMD registers.
Take SSE as an example: each register has four 32-bit lanes. Computing SHA-256 four times in parallel makes sense. We can define a new hash algorithm for computing the hash of a single file as slicing the input into four pieces, computing the hash of each of the four pieces (in parallel), then produce the final result by hashing the final four sub-hashes together. Obviously, this would be a new hash function, not matching a normal SHA-256.
Are there security problems with such a design that wouldn't exist with a normal hash algorithm?