while i suppose the second is a valid resonance structure, it is not nearly as major a contributor as the first set you drew. if you wanted to go wild, you could start with the upper left structure and move the electrons just in the most distal double bond and move those electrons on to the terminal carbon atom. Then you could reverse course and move those electrons on to the penultimate carbon atom. All without disturbing the other double bond or the carboxylate group.
But I would say the four structures you drew at top are the major ones, and I would leave it at that.