I don't know how well this would scale on 14MB sets, but this might be a possible solution using Set::Scalar.

Yes, Eily had the most efficient solution. There's no need to create the 3 sets :-(

use Set::Scalar;

my %hash_4;
my $set_1 = Set::Scalar->new(keys %hash_1);
my $set_2 = Set::Scalar->new(keys %hash_2);
my $set_3 = Set::Scalar->new(keys %hash_3);

my $intersect = $set_1 * $set_2 * $set_3;

for my $key (@$intersect) {
    push @{$hash_4{$key}}, $hash_1{$key}, $hash_2{$key}, $hash_3{$key}
+;
}
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