Could a candidate for Vice President run with more than one Running Mate for two different parties?

This might sound like an odd question but I have a reason for asking. A number of people have raised the possibility that, if Romney gets the Republican Party's nomination, an obscure rule might allow Paul supporters to put Ron Paul on the ticket as a VP candidate. So this got my mind thinking: I know that in the State of New York it is possible for a candidate to run on more than one party's ticket and this often happens in that state. For example, if the Conservative Party of New York endorses a Republican candidate he could show up on the ballot on two lines and the party officials simply add the votes cast with him as a Republican and with him as a candidate for the Conservative Party of New York. Seems rather simple, right? But what if you had a situation where a VP candidate was running on both the Republican Party ticket with Mitt Romney AND on the Libertarian Party ticket with a different person? Could we, in theory wind up with Obama as President and Ron Paul as Vice President?

Just an idea.