We can, of course, at least in theory. But the cost is staggering. The cost of providing, say, 2 million net square feet of office space in one 80-story building is something like 30-50% more than providing the same area in two 40-story buildings. And once you get into the realm of super-tall buildings, the marginal cost of adding one more floor becomes breathtaking.
Those additional floors affect the cost of every floor below. Add a floor, and the entire structure must be a bit stiffer (wind load as well as weight-bearing capacity) -- so thicker columns, with more concrete and/or steel. Water lines (for plumbing and sprinklers) must be thicker in order to bear the crushing weight of what is, in effect, a column of water a thousand feet, or two thousand feet, or whatever tall. And of course, pumping becomes a more difficult issue as the building gets taller. Stairwells must be pressurized and air-locked, both for fire safety and so they can be opened against wind presure. And the list goes on and on.
But the biggie is elevators. Inevitably, no matter how fast and sophisticated your elevator system, the higher you go, the more elevators you will need. One additional elevator for each two floors added is a reasonable guess (even though all the elevators won't go all the way to the top. Let's say increasing your 159-story building to 160 stories requires one additional elevator going all the way to the top. Let's say that the 160th floor has a net rentable area of 10,000 square feet (given that the building tapers to relatively small floorplates near the top). That one additional elevator uses up about 100 square feet of what would otherwise be rentable area on all 160 floors. So you gain 10,000 rentable square feet, and lose 16,000. Add the cost of constructing that 160th floor itself, plus the additional costs applicable to the structure of the entire building, and you see the problem.
This is not to disparage super-tall buildings, of course. I'm fascinated by them, too. And even if they don't justify their costs to the corporation and/or government building them, their marketing value must be considered. But their comes a point where the marginal cost of one more floor becomes absurd. Whether that point is 80 floors, 100, or more, depends on the goals and capacities of the builders. But 160 floors rarified atmosphere, figuratively if not literally.
Ahh, but you forget the spire at the top. Those are good for a few floors in height at relatively little cost.