How can I pull out lines between two patterns that are themselves on different lines?

You can use Perl's somewhat exotic .. operator (documented in perlop):

    perl -ne 'print if /START/ .. /END/' file1 file2 ...

If you wanted text and not lines, you would use

    perl -0777 -ne 'print "$1\n" while /START(.*?)END/gs' file1 file2 ...

But if you want nested occurrences of START through END, you'll run up against the problem described in the question in this section on matching balanced text.

Here's another example of using ..:

    while (<>) {
        $in_header =   1  .. /^$/;
        $in_body   = /^$/ .. eof();
	# now choose between them
    } continue {
	reset if eof();		# fix $.
    }

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