If your packers and movers need to walk multiple times through more stairs, there will be a loss of time for both you and your packers and movers.
Local moving companies may bill you with the hourly charge when relocating locally. But if your relocation process becomes lengthier, the more time your moving companies take carrying things using the stairs, then you need to spend more money.
Please remember that even if the apartment has a lift, if your moving company is compelled to wait a long time for it since it is not particularly allocated for them, you have to pay more for the time they missed.
If the packers and movers will have to operate additional difficult to shift large furnishings and big cartons up and down the stairs, as a matter of fact, the total difficulties of the house relocation will rise, and you can assume that the relocation expense will also rise as well.