Then that's precisely the problem, that default templates only work up to 3 monitors.
I agree that if you're only using that template, the win+left/right is probably a better solution than GridMove (at the time GridMove was developed, that option didn't exist ;) ).
If you'd like to use GridMove for more than 3 monitors, just edit the grid file you're using, copy and paste the groups for one of monitor3 and change them to monitor4, and update the number of groups at the top.
As an example, the 2 part grid (
https://github.com/jgpaiva/GridMove/blob/master/Grids/2%20Part%20Vertical.grid) would be something like this:
[Groups]
NumberOfGroups = 12
[1]
TriggerTop = [Monitor1Top]
TriggerLeft = [Monitor1Left] + [Monitor1Width] / 2 - 50
TriggerBottom= [Monitor1Top] + 35
TriggerRight = [Monitor1Left] + [Monitor1Width] / 2 + 50
GridTop = Restore
GridLeft = Restore
GridBottom= Restore
GridRight = Restore
[2]
TriggerTop = [Monitor1Top]
TriggerLeft = [Monitor1Left]
TriggerBottom= [Monitor1Bottom]
TriggerRight = [Monitor1Left] + [Monitor1Width] /2
[3]
TriggerTop = [Monitor1Top]
TriggerLeft = [Monitor1Left] + [Monitor1Width] /2
TriggerBottom= [Monitor1Bottom]
TriggerRight = [Monitor1Right]
[4]
TriggerTop = [Monitor2Top]
TriggerLeft = [Monitor2Left] + [Monitor2Width] / 2 - 50
TriggerBottom= [Monitor2Top] + 35
TriggerRight = [Monitor2Left] + [Monitor2Width] / 2 + 50
GridTop = Restore
GridLeft = Restore
GridBottom= Restore
GridRight = Restore
[5]
TriggerTop = [Monitor2Top]
TriggerLeft = [Monitor2Left]
TriggerBottom= [Monitor2Bottom]
TriggerRight = [Monitor2Left] + [Monitor2Width] /2
[6]
TriggerTop = [Monitor2Top]
TriggerLeft = [Monitor2Left] + [Monitor2Width] /2
TriggerBottom= [Monitor2Bottom]
TriggerRight = [Monitor2Right]
[7]
TriggerTop = [Monitor3Top]
TriggerLeft = [Monitor3Left] + [Monitor3Width] / 2 - 50
TriggerBottom= [Monitor3Top] + 35
TriggerRight = [Monitor3Left] + [Monitor3Width] / 2 + 50
GridTop = Restore
GridLeft = Restore
GridBottom= Restore
GridRight = Restore
[8]
TriggerTop = [Monitor3Top]
TriggerLeft = [Monitor3Left]
TriggerBottom= [Monitor3Bottom]
TriggerRight = [Monitor3Left] + [Monitor3Width] /2
[9]
TriggerTop = [Monitor3Top]
TriggerLeft = [Monitor3Left] + [Monitor3Width] /2
TriggerBottom= [Monitor3Bottom]
TriggerRight = [Monitor3Right]
[10]
TriggerTop = [Monitor4Top]
TriggerLeft = [Monitor4Left] + [Monitor4Width] / 2 - 50
TriggerBottom= [Monitor4Top] + 35
TriggerRight = [Monitor4Left] + [Monitor4Width] / 2 + 50
GridTop = Restore
GridLeft = Restore
GridBottom= Restore
GridRight = Restore
[11]
TriggerTop = [Monitor4Top]
TriggerLeft = [Monitor4Left]
TriggerBottom= [Monitor4Bottom]
TriggerRight = [Monitor4Left] + [Monitor4Width] /2
[12]
TriggerTop = [Monitor4Top]
TriggerLeft = [Monitor4Left] + [Monitor4Width] /2
TriggerBottom= [Monitor4Bottom]
TriggerRight = [Monitor4Right]
I copied groups 7, 8 and 9 into 10, 11 and 12, updated them to monitor4, and then updated the NumberOfGroups at the top from 9 to 12.