"Balancing" positive and negative literals in 2-sat

Question

I saw in an answer to this post that it is possible to construct 3-sat clauses with extra variables such that the number of positive and negative literals for each variable are equal. Does anyone know of a construction for 2-sat instances to accomplish this or know it to be impossible? I have been trying, but all I have been able to achieve is narrowing it down to the case where each variable occurs exactly 3 times using the same construction accomplishing this for general SAT. Then of course the difference between positive and negative literals would be exactly 1.