There is one problem. Being able to buy partial stacks, would, allow people who have steady influx of items to control the market since they could just set a few stacks of something for a price, buy everything significantly cheaper than that price, and just keep refilling those stacks as the partial sales go through.

Instead I'd like to see people being able to list a whole stack of items at a total price instead of a unit price (so you could list 99 of an item for 106 gil, instead of either having to sell the whole stack at 1 gil each (at a 5% loss compared to selling it to NPC) or 2 gil each (being the same price as the NPC)) with having the unit price reflecting this (eg 1.07 gil per item). The total cost would still have to be a whole gil. In this way, it would give more pricing freedom for larger stacks of items (essentially allowing them to set a lower per unit price) without penalizing people who might only want to sell a few items at a time.