I would like to install a tool like EtherPad on my debian server, that uses PHP and MySQL as backend.
I found etherpad-lite, that is written in node.js and PiratePad, which is only an online platform but I would need a script I could install on my server
PHP cannot solve the "collaborative editor problem" easily because it spawns a new process for each visitor of a site so the memory space is not shared meaning you would have too much latency from database read/writes.
So short answer, no, PHP is not going to solve your problem. Why not just install Etherpad?