I've found that the threshold depends not so much on number of APs but on number of simultaneously active users/devices (arguably the ratio of those per AP, rather than total).

An office of 30 people sharing 3 APs will encounter problems even if those same APs would have worked just fine for a family of 4 living in the same space.

I've even found this to be true in a residential setting with consumer APs, where reducing the number of devices (by plugging into wired ethernet things that don't often move, such as media players and printers) tends to improve range and throughput for others, without adding more APs.