Legal Question in Civil Litigation in California

Potentially. If the other party cooperates, you may be able to file a Stipulation to Continue Trial. You should first check with the court department to determine whether a formal motion would be required, or whether the parties could just submit the Stipulation to Continue Trial. The department might require an "ex parte motion to continue trial," and the Stipulation to Continue Trial would be helpful to show that both parties want the trial continued.

Typically, you need to show a good reason for continuing the trial. You should take a look at Rule of Court 3.1332: http://www.courtinfo.ca.gov/cms/rules/index.cfm?title=three&linkid=rule3_1332

This article may also be helpful, but make sure any citations are up-to-date, since the article is several years old: http://www.lacba.org/Files/LAL/Vol31No1/2466.pdf

I would look into a "stipulation to continue trial" just as my colleage has mentioned.

The adverse party may ask the Judge to continue the trial If there has not been a continuance before, and there is a decent reason for continuance, most judges allow a continuance.

It appears my colleagues did not read your question properly. With a May 20 trial date, there is VERY little chance that a continuance would be granted unless YOU agree, AND there is good cause for the continuance, OR there is extremely good cause for a continuance, such as the other side's attorney is suddenly incapacitated or has some REAL emergency. The chances of a continuance being granted to the other side if you want the trial to go forward on the 20th, are almost zero unless it is a really serious reason that the other side MUST move the date.