I’m in the ACT, not NSW, but I would be surprised if you could purchase part of the common property outright. A grant of exclusive use is certainly possible. To get part of the common property converted to being part of your lot would, I expect, require having the strata plan redrawn and lot entitlements reallocated on the basis of a new valuation in which there might be winners and losers. In the ACT at least there is a very high threshold for doing that, perhaps an unopposed resolution, from memory.
I would expect a bylaw for exclusive use for the owner of your lot would be easier and just as effective.