The following only calls _v 15 times. ;) Of course, splice (or its optimized equivalent) and %seen are still called 29 times, but that's a far cry less than the possible 41. Also, even with the original code, the (presumably expensive) callback is only called 15 times.

   local *_r = sub {
      my @v = @_;
      return if not $cb->(@v);
      return if @v == 1;
      for (0..$#v) {
         my @v_ = @v;
         splice(@v_, $#v-$_, 1);
         _r(@v_) if not $seen{join $;, @v_}++;
      }
   };
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It breaks the rule "A,B,C should be generated before A,C", but the following might allow you to break down the problem such that your requirements can be loosened:

my ($u_set1, $u_set2, $common) = extract_common($set1, $set2);
my $psetc = powerset($common);
my $pset1 = product($psetc, powerset($u_set1));
my $pset2 = product($psetc, powerset($u_set2));
my $pset = union($pset1, $pset2);
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