The easiest way to store multiple values in a hash is to have the hash value be an array reference. An array reference will automatically be created if you just treat it as one:

my @words = qw/FrobniZZ Shiftboard CocaCola ShiftBoard/;
my %cases_found;
for my $word (@words) {
    push @{ $cases_found{ lc $word } }, $word;
}

for my $lc_word ( sort keys %cases_found ) {
    print "$lc_word found with these cases: ",
        join( ', ', @{ $cases_found{ $lc_word } } ), "\n";
}
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