Only 1 y label in GNUplot multiplot

Plot the individual panels of reduced size without labels but with border, tics and title, then define a full-sized panel with labels but without border, tics and title.You may have to plot a dummy function (1/0).

The simplest way is to make the first plot, then turn off the y label:

set ylabel 'foo'
set multiplot

plot 'data1.dat'

unset ylabel

plot 'data2.dat'
plot ...

unset multiplot

This will make the x-dimension of the first plot different from that of all the other plots, so you may have to play with the margins if you want all the plots the exact same size.