No you do not need to request an extension for an amended return. Wait for the original return to be fully processed and then amend it.
Wait until your original return has been fully processed before you amend, and make sure you have saved a pdf of the original return before you amend. (If you do not save it as a pdf, the amended return will overwrite the original, and the original will be lost forever)
See this TurboTax support FAQ for amending a tax return -
CURRENT YEAR
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-federal-tax-return-current-year/L7eS6o1qh_US_en_US?uid=lfunevhk