top of page 18.
http://www.workforcesecurity.doleta.gov/foreign/pdf/perm_faqs_3-3-05.pdf
What this says is that the company can file LC for a different position as long as it is at least 50% different for what you did/are doing right now. Because you do not have to be working in the position that your labor is filed for; and because the labor cert has nothing to do with the individual and everything to do with the company; filing multiple LCs for the same individual is not unlawful. Now would your application be more likely to be audited? One may argue yes. Who knows? No one does. This whole process is neither scientific nor orderly - it's highly SUBJECTIVE.
One may be able to convince their company to file a second LC using PERM for a 50% different position, IF they are presently stuck at the BEC .
However...
finding a company that would file more than two LCs or even two, both or more in PERM is highly unlikely only because why would they bother? Plus they have to recruit separately for each LC. On top of that even if you pay they have to spend time reviewing resumes/possibly conducting interviews etc. And time is money.
Additionally lawyers are always ultra cautious about these things especially immigration lawyers who just file cases (I mean think about it) MOST of them don't want to take on anything that is beyond straight forward 3rd grade level...cos there is more than enough business for them. So they will play along with your company if they think they might need to type an extra letter or make it 20X more expensive deterring your chances.
But bottom line is it can be done and there is nothing illegal or shady about it. And if a company GENUINELY wants you bad enough they will go to all lengths. If they can live without you they will show you their standard policy...blah blah blah...and give you excuses.