Before the expiration of the time prescribed for the assessment of any local tax, if both the commissioner of the revenue or other assessing official and the taxpayer have consented in writing to the tax assessment after such time, the tax may be assessed at any time prior to the expiration of the period agreed upon. The period so agreed upon may be extended by subsequent agreements in writing made before the expiration of the period previously agreed upon. Whenever such an extension is agreed upon, it shall likewise extend the period relating to the collection of local taxes pursuant to § 58.1-3940 and applications for correction pursuant to § 58.1-3980.