You can amend a return as many times as necessary.
You should wait until the first amendment is processed and accepted by the IRS before sending in the second one to ensure they are done in the proper order.
You will have to remove/delete form 1040X from your taxes without removing prior changes made. Then you will start the amendment process again and add the new 1099.
You may track status
of the first amended one using the below link:
https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1
See this TurboTax support FAQ for amending a tax return - https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed
The most reliable way to do this is to let the program delete the 1040X form for you:
Thanks to user jeking3 for this solution