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Can I use one repsberry pi 3 to control 4 printers?

In short, yes you can and the Pi 3 has 4 USB ports. http://blog.patshead.com/2016/02/contro ... print.html

For that matter, you could slap a 7 port powered hub on it and just get nuts.

g.

You would be limited by the processor power and memory. People do use one Pi for two printers. The Pi3 has four processors where the Pi2 had two. So you should be able to manage four printers. It might run out of memory but you are running four instances of the same program -- the program code only needs to be in memory once -- so the only limitation is the data buffers. It's cheap and easy to try; if it stutters too much buy another Pi.

The article I linked to has processor utilization metrics. 20% for 2 printers AND 2 video feeds. 4 printers alone would be a piece of cake.