I'm not at all sure if this is what is required. It only takes tuples of all the same letter if they are at the start of the string.

use strict;
use warnings;

my @sets = qw{
   AAAAADDDDDEFFGMMSSTVVVVV
   AADDDEEEEFFFFGGMMMMMMMMMMSTV
   };

foreach my $set ( @sets )
{
    print qq{$set\n};
    my @tuples;
    while ( length $set >= 4 )
    {
        if ( $set =~ m{^(.)\1{3}} )
        {
            push @tuples, substr $set, 0, 4, q{};
        }
        else
        {
            my @boundaries = ( 0 );
            push @boundaries, pos $set while $set =~ m{(.)(?=.)(?!\1)}
+g;

            last if scalar @boundaries < 3;

            push @tuples, join q{},
               reverse
               map substr( $set, $_, 1, q{} ),
               reverse @boundaries[ 0 .. 3 ];
        }
    }

    print qq{     $_\n} for @tuples;
    print qq{     Left over: $set\n} if $set;
}
[download]

The output.

AAAAADDDDDEFFGMMSSTVVVVV
     AAAA
     ADEF
     DDDD
     FGMS
     MSTV
     VVVV
AADDDEEEEFFFFGGMMMMMMMMMMSTV
     ADEF
     ADEF
     DEFG
     EFGM
     MMMM
     MMMM
     MSTV
[download]

I hope this is of interest.