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One AP per 5 active devices, give or take.Probably never heard of professional office routers. You can have several times that.
Even if working in a 100+ person company, all such companies I've been already have all the company wide wi-fi and APs the need, so I don't see why the parent's company couldn't.
As for "ensuring they do proper hand-off as you move around the office", it's much easier with APs than plugging and unplugging ethernet cables -- which was the alternative we were discussing.