Yes. As long as your attorney is still ready to proceed to trial, s/he can file a new demand. You should discuss this further with your attorney. Good luck!
`Karen J Tufte
Board Certified Criminal Trial Attorney
You can file a demand for speedy trial frequently. In Barker v. Wingo, the U.S. Supreme Court stated one of the factors was that the defendant pressed for a speedy trial (not necessarily a motion to dismiss but to press for a trial.) A Florida attorney can more accurately respond about local law. You should speak to your attorney about this.
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When prosecution is commenced, an accused has a right to a speedy trial without demand. It sounds like your attorney actually filed a demand for speedy trial, most likely after initially waiving your right to a speedy trial. When you file a demand for speedy trial you are letting the Court know I AM READY for trial regardless of scheduling issues. I am not sure what exactly happened with your case but often times a judge won't continue a case after you demand speedy trial.
To specifically, answer your question, nothing in the rules of criminal procedure precludes a second demand for speedy trial.
You can file a demand at any time you're ready to proceed, even if the normal "speedy trial" time frame has passed. If you and your lawyer and ready to proceed, speak with him/her about filing the demand.