Yes, you can amend your return more than once.
Note that your second amended return will start with the information from your first amended return, not your original return (since you did it in TurboTax).
This may make the numbers on the second 1040X look odd, until you realize that you are amending an amended return, not the original.
Also, I don't know if this is a possibility, but you want to be sure that the first amended return has been processed. Since the IRS has not been handling paper returns, this may be difficult to judge, so I encourage you to write at the top of the second 1040X that this is a second amended return, and the first was filed on (the date you mailed it).
You might also add that note to the explanation of why you are amending the return (bottom of page 2) - I want to give the IRS person handling the second 1040X every opportunity to notice that there was a prior amendment.
Basically, you need to go into forms mode and delete the 1040-X. Then the program will treat the return "AS IF" it was the originally filed return. I would highly suggest you print out the amended return first, before you delete the 1040-X so that you have it for your records should a need for it arise with the IRS.