I think the best you can do is use IO::Handle and then call getline on it instead.

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;
use IO::Handle;

open my $fh, '<', $0
    or die "Can't read myself: $!\n";
my $self = { fhFrom => $fh };
my $fh2 = ${$self}{fhFrom};
my %line_from;
chomp( $line_from{var} = <$fh2> );
chomp( $line_from{expr} = <${$self}{fhFrom}> );
chomp( $line_from{graff} = <$$self{fhFrom}> );
chomp( $line_from{getline} = $self->{fhFrom}->getline );

print Dumper \%line_from;
__END__
$VAR1 = { 
          'var' => '#!/usr/bin/perl'
          'graff' => 'GLOB(0x504290)',
          'getline' => 'use strict;',
          'expr' => 'GLOB(0x504290)',
        };
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I don't know the nuts and bolts of it, but once the "stuff" inside <stuff > gets "too complicated", it treats it like glob.