Runs without any problems with cartridges from other manufacturers. However, I would probably not buy another HP for other reasons... I have to connect the laptop to the printer via WLAN for space reasons. And this is not very reliable.
This is my individual, personal experience. The toners are not blocked by hp, but hp indicates that they are third party. This is saved and hp no longer provides a guarantee for possible repairs. I also found that the original hp toners printed more pages than the compatible toners of the same number.