The first question that came to mind was whether we are talking about black raspberries or red? Red's are usually pretty tough, but black ones don't do well where reds have grown... or was it blackberries. You may need to google that one. I have grown both, but never at the same time and the second time for BR was a disaster... I guess the bacteria was still in the soil. I am no expert and it has been many years now.

My choice would be to grow them alone and use some good mulch to hold moisture and feed the soil as it rots.

And neither is recommended as far south as we are. I have black and purple planted last year myself. And admittedly it was their first fruiting year, but I was SO not impressed. Giving them one more year, then out they go, if I'm not impressed.