Is there such a thing as "F4" a range?
If you highlight both components of the range in edit mode, F4 will
cycle through the various absolute and relative syntax on both at the
same time. For example, A1

1 becomes $A$1:$D$1, then A$1

$1, then
$A1:$D1, then A1

1 again. If you need a mix of absolute/relative
syntax (e.g. $A$1

$1), you need to highlight each component and cycle
F4 separately -- or simply type what you want.