Okay, we need a bit of sillyness here ...

use 6; # require perl v6
use List::Util qw/reduce/;

@foobar = @{reduce{[@$a ^+ @$b]}\(@foo, @bar, @baz, @etc)};
[download]

Note: Untested :-)

Update: Oops, pushed the wrong button. (Note to self: In the future, type the non-silly version first ...)

What you want is something that is easily extendable -- "more than two 4 element arrays" suggests that to me, at least. So, work with lists:

use List::Util qw/reduce/;

@foobar = @{reduce{[map $a->[$_]+$b->[$_], 0..@$a>@$b?$#$a:$#$b]}
                   \(@foo, @bar, @baz, @etc};
[download]

Unfortunately, this is also untested, as I am at work with no List::Util installed ... also unfortunately, this is still a lot of typing, and it creates a lot of anonymous arrays, so don't use it mindlessly :-\

The Sidhekin
print "Just another Perl ${\(trickster and hacker)},"