If you want a finer level of control than a redo, you can pull the keys function out of the loop and then iterate over an array with a counter. Then you will have the ability to manipulate the counter however you wish. Here's a simplistic example:

use strict;

my %hash = (test1 => 1, test2 => 2, test3 => 3, test4 => 4);
my @array = sort(keys(%hash));
my $counter = 0;
my $resetter = undef;
my $resets = 0;

while($counter <= $#array){
  if(defined($resetter)){
    $counter = 0;
    $resets++;
  }
  $resetter = undef;
  print $hash{@array[$counter]};
  $counter++;
  $resetter = 1 if $counter > 2 and $resets < 2;
}
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If all you need is the ability to restart the loop, the for/redo suggestion above requires a smaller code change.