Can a defendant amend his plea to a lesser charge?

"We note further that our decision does not foreclose the parties from agreeing that the defendant may be convicted of a lesser offense not necessarily included in the original charge. When the parties consent to such a procedure, with or without formal amendment of the pleadings, neither can claim unfairness, and the prosecution's role in determining the charges is not improperly compromised. Indeed, there may be many cases in which both parties are persuaded that their best interests lie in such a procedure. Finally, nothing in our holding prevents the defendant from arguing in any case that the evidence does not support conviction of any charge properly before the jury, and that complete acquittal is therefore appropriate." (People v. Birks, supra, 19 Cal.4th 136, fn. 19.)