It's not Net::OpenSSH, but Net::SSH2 can do multiple commands thru it's channel's shell() method. Try it, if you can't find a Net::OpenSSH solution. Keys Auth logins is also supported.

#!/usr/bin/perl
use warnings;
use strict;
use Net::SSH2;

# assuming a user named 'z' for demonstration 
# connecting to localhost, so you need your sshd running

my $ssh2 = Net::SSH2->new();
$ssh2->connect('localhost') or die "Unable to connect Host $@ \n";
$ssh2->auth_password('z','ztester') or die "Unable to login $@ \n";

#shell use
my $chan = $ssh2->channel();
$chan->blocking(0);
$chan->shell();

print $chan "ls -la\n";
print "LINE : $_" while <$chan>;

print $chan "who\n";
print "LINE : $_" while <$chan>;

print $chan "date\n";
print "LINE : $_" while <$chan>;

$chan->close;
__END__
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