Apples are pretty tough and will knacker a juicer a lot quicker than you want.
If you want to use blackberries that way they wuld be fine, but you might be better off using the turbo cider method, get some apple and blackberry (or just apple and add juiced blackburies) and do it that way, there are plenty of turbo cider guides on here, just use whatever juice you want!
If you have lots of apples to spare, you may want to find someone with proper set up, here in Wales there's a good cider and perry group whereby you give the fruit, take away some juice to ferment and give the rest to them, much easier and gives more juice.