There is nothing stopping you from buying and owning all the units in an apartment block. However whether you get them at a good price may depend on many factors including where in the property cycle you are in, the demand for those properties at that time, and interest rates at the time.
When you buy one unit you become a part owner in the common property (e.g. hallways and stairwells, driveways and gardens). So if you end up owning all the units in the block you will also own all the common property.
In effect unit block needs to have a strata manager to take care of the common property and issues relating to the entire complex, and each owner votes on various decisions of how certain issues are taken care of. If you are the only owner for the whole complex you in theory don't need a strata manager for the complex, as you can decide on these matters yourself without having to take a vote. You would also have to take out insurance for the whole complex, including each separate unit plus all the common areas.
Even though you would own the whole complex it is a good idea to still keep the complex strata as this will make it easier in the future to be able to sell individual units rather than the whole complex as one large property.