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An extension request is called a continuance. This would mean filing a Motion for Continuance and serving it to the other parties, and setting it for a hearing either the SAME day as the hearing one wishes to extend, or earlier (earlier is much preferred). The parties should have at least 3 days notice to the hearing.
You can find a sample HERE.
It is impossible to dismiss hearing on a valid motion requested by another party. So likely, this will not be possible - it is more likely that the Court will grant the continuance, if this is filed timely and properly, and there is a good reason to request it.
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