Hmmmm....good point. Well, you can fix part of it with (?=.*\bfred\b (\w+)), but avoiding matching none of the targets is still a problem. The way I suggested will always get three matches because it says find "zero or more of this". That means either you can't actually find out how many non-empty matches you got, or you can only match when all the targets are present. Separate matches in a loop, as suggested by several others, is the way to go. Here's my take, redux:

$string = "This is bLarney rubble and his friends joe rockhead and fre
+d flintstone";
$count = 0;

for $target (qw(fred barney joe)) {
    if ( $string =~ /(?=.*\b$target (\w+))/i ) {
        push @elements, $1;
        $count++;
    }
    else {
        push @elements, ''; # as a placeholder
    }
}

if ($count >= 2) { print join('_', @elements), "_inc\n" }
else             { print "Didn't find at least 2 elements in the strin
+g\n" }

# prints flintstone__blockhead_inc
# change 'joe' to 'moe' and you get > Didn't find at least 2 elements 
+in the string
[download]

There ought to be something useful in there. :-)

I missed the '2 or 3' requirement on first reading of the OP. For the sake of maintainability if nothing else, a looping (loopy?) approach may, as you say, be the way to go.

However, there is a simple way to deal with the undefined values produced by zero-quantified captures:

>perl -wMstrict -le
"my $bound = qr{ (?<! [\w-]) }xms;
 my $A = qr{ (?= .* $bound A \s+ (\w+)) }xms;
 my $B = qr{ (?= .* $bound B \s+ (\w+)) }xms;
 my $C = qr{ (?= .* $bound C \s+ (\w+)) }xms;
 my $extract = qr{ \A $A? $B? $C? }xms;
 print '-------------------';
 for my $line (@ARGV) {
   my $s = join '_', my @got = grep defined, $line =~ $extract;
   $s = 'no match' if @got < 2 or @got > 3;
   print qq{'$line': '$s'};
   }
"
"B Bee C Cee A Aye"  "foo C Cee bar A Aye baz B Bee zzz"  "A Aye B Bee
+"
"C Cee foo B Bee"  "xxx C Chuck yyyy A Able zzz"  "A Aye A Aye B Bee"
foo  "A Aye"  "A Aye pseudo-B Bee"  "A Aye XYZB Bee"  "A Aye A Aye A A
+ye"
-------------------
'B Bee C Cee A Aye': 'Aye_Bee_Cee'
'foo C Cee bar A Aye baz B Bee zzz': 'Aye_Bee_Cee'
'A Aye B Bee': 'Aye_Bee'
'C Cee foo B Bee': 'Bee_Cee'
'xxx C Chuck yyyy A Able zzz': 'Able_Chuck'
'A Aye A Aye B Bee': 'Aye_Bee'
'foo': 'no match'
'A Aye': 'no match'
'A Aye pseudo-B Bee': 'no match'
'A Aye XYZB Bee': 'no match'
'A Aye A Aye A Aye': 'no match'
[download]

Nice. Had to ponder that a moment to follow it. :-)