In the main multi lights from multi switches means lights all connected to come on together and the two switch wires go to first switch the from there three wires go to all other switches, first and last switch is called two way, those between first and last are called intermediate.
There is a modern system using two wires between electronic switches, using that all need to be same make and system first switch called master rest called slaves.
There is a system where each switch returns to ceiling rose, but it needs four connections plus earth in ceiling rose and so one needs special emergency light ceiling roses to get extra wire.
So no system I have met would do as yours does, so not a clue how wired. There is also RF switching where sometimes a battery is used and sometimes the moving of the switch generates enough power to transmit to master, think latter is MK.
So good news is there will be a way without running extra wires to cure problem, bad news is without testing don"t know which of the options will work.
I wanted to be able to switch bedroom light on/off from in my bed, did not want to run new wires down wall, so fitted a Mihome switch which can have three remote controls. So remote by bed. However the switch is rather big, it will not fit in plaster depth box, so one does have to be careful.