You can increase the size of the basement by adding on to it where the crawl space part is. It's a lot of digging, supporting, and concrete forming and pouring in a confined area. It is not easy and cheap. Cost is decision you will have to make. Contact a local basement contractor about it.
I understand this to be a split level home with a partial basement and the rest is crawlspace. If you are also asking about trying to increase the height of the 7' basement by lowering the footings or even adding on top then I think you are definitely in a cost prohibited change. If you convert the crawl space portion to a basement, then you could do it at 8'+ and have a step down between the two.
Good luck and post back with what a contractor tells you after looking at it, what you do, and what it costs.