I'm not sure if I'm missing the point, but here's one example of a routine that uses lexical scoping, named blocks and goto to invoke different segments of code in the routine each time it's called.

use strict;
use warnings;




{
    my $location = "FIRST";
    sub jumparound {
        goto $location;
        FIRST: { 
            print "First segment.\n"; 
            $location = "SECOND";
            return;
        }
        SECOND: {
            print "Second segment.\n";
            $location = "FIRST";
            return;
        }
    }
}

jumparound();
jumparound();
jumparound();
[download]

And the output is:

First segment.
Second segment.
First segment.
[download]

This snippet seems to satisfy "preserve the values of their local variables between successive calls."

It also satisfies "appears to be like subroutines with multiple entry and exit points."

But I haven't read Knuth (and I'm beginning to feel like it's high time I do), so I'm not sure if my snippet satisfies all of the requirements.

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