Filling in the missing pieces in the approach suggested by Gangabass above:

#!/usr/bin/perl

use strict;
use DBI;

my $dbh = DBI->connect( ... );

my @val1_set = qw/foo bar baz quz/;

my $sth = $dbh->prepare("select val1,val2,val3 from atable where val1=
+?");
my @result_set;

for my $val ( @val1_set ) {
    $sth->execute( $val );
    my $result = $sth->fetchall_arrayref;
    push @result_set, $result;
}
for my $i ( 0 .. $#val1_set ) {
    print "Results for val1=$val1_set[$i]:\n";
    if ( ref( $result_set[$i] ) ne "ARRAY" or
         @{$result_set[$i]} == 0 ) {
        print "__EMPTY_SET__\n\n"
    }
    else {
        for my $row ( @{$result_set[$i]} ) {
            print join("\t", @$row ),"\n"
        }
        print "\n";
    }
}
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That will work no matter how many rows get returned (0, 1 or more) on each iteration over the set of "val1" values. For any non-empty return from the execute() call, the "fetchall_arrayref" always returns a reference to an AoA (a set of 1 or more rows, with each row containing a set of 1 or more columns or fields), so you have to dereference the set of rows, and then for each row, dereference the set of columns.

(update: And in this case, since the result set is an array that is built up over some number of execute calls, you are starting with an AoAoA, so the sample code uses $i to iterate over the top-level array.)