Best to run a test roll through your camera and establish the ideal dev time & EI for yourself.
At one time both Kodak and Fuji made special high speed E6 films designed to give their best results at 1600 EI but in fact their true base speed was 40 EI and they needed push processing, at 400EI they were lifeless and low contrast. Their emulsions were optimised for push processing and the Ilford Delta 3200 works in the same way.
Most people aren't aware that XP2 Plus is excellent push processed in C41 chemistry. I used a lot of XP1 push processed to Ilford's recommendations in their data-sheets shooting Rock concerts with excellent results. However labs didn't like XP1 because it used non standard (longer) C41 development times and that caused issue for customers, I processed my own so it wasn't a problem.
So when Ilford released XP2 it was an emulsion designed for the shorter standard C41 development time that all labs use but they dropped all mention of push processing. I just carried on pushing the new emulsion and it was still excellent. I had a discussion about this on a business trip to Mobberly with a senior research chemist (mid 1980's) and they conformed XP2 could be push processes but that apart prom Pro labs the average High Street labs didn't have the capability which had in fact been the problem with XP1
Ian