I’d be guessing the process should be similar to that when attic conversions etc take place, described elsewhere on these forums.
The owners are appropriating common property and normally you’d be required to purchase, lease (via exclusive use clauses) if you’re using land/airspace owned by the OC. Although you might want to check your plan of subdivision to be sure that the space below floor level is definitely OC (it usually is, but some aren’t: lot extends ‘infinitely’…)
I’d also put the onus on the owners to provide the OC with relevant permits and surveyor signoffs that the work is to code, and no subsidence or other damage to the building is likely as a result of the works before even thinking about purchase/lease of the space.