The grounds for summary judgment may not change from initial motion, but presumably the evidence has. If the motion is the same as before w/o new evidence discovered after the last motion, you may be able to attack the motion on the grounds that they are really making a motion for reconsideration of the prior motion, unless they are adding new information not known when the earlier motion was heard.
For thorough discussion of this issue see this CA Bar publication from 2006: http://archive.calbar.ca.gov/%5CArchive.aspx?articleId=81663&categoryId=81622&month=11&year=2006. You should, of course, review later case law and verify current statutes.
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The terminology might be different, but you could be describing what is often referred to as either a "motion to reargue" or a "motion to renew". Generally speaking, a motion to reargue is based on the same argument and evidence that was first presented, but the moving party is trying to show that the court misunderstood the evidence (fact) or misapplied the law, so as to come to an originally erroneous decision. It can not be based on new arguments or theories. A motion to renew is based on "new evidence" which the moving party must show was not only not in its possession at the time of the previous motion, but also there is a reasonable explanation as to why that movant could not have obtained that evidence before making the first motion. I defer to my CA colleagues to advise if the standards for such motions are different in CA. Your opposition would be to argue that the motion should be denied for failing to meet the procedural and/or substantive requirements as touched upon above. Good luck.
Assuming the first summary judgment was denied and there is a triable issue of fact then you may want to make a collateral estoppel/res judicata argument which is a legal doctrine which prevents relitigating the same claim or issue after a court has already made a ruling. I think more information is needed to fully answer your question.
This is my opinion and should not be construed as legal advise for your specific case as there are many more facts which you have not provided.