In other words, can one have two Vietnamese passports at the same time?
Since I dont really understand your question, I assume that there are two cases for this:
Case 1: If you mean to ask whether or not you can use two passports to enter Vietnam (i.e one is Vietnamese passport and the other is US passport), you CAN TOTALLY USE one of them to enter the country. If you choose to use Vietnamese passport, you must follow the regulations of Vietnam government. The same goes for US passport that you must also follow US government's regulations.
Case 2: If you mean to ask whether or not you can use two Vietnamese passports at the same time (literally described in your question above), then the answer is No. You cannot have two valid passports at the same time. Vietnam's government does not allow this to happen. If you apply for a new passport, the old one will be invalid right at the time you get a new one.
Note: If you use one passport for entry and the other for exit from Vietnam, then it is illegal according to Vietnam laws.
1Hi, welcome to Travel.SE! Most of us here believe the most useful answers are those that can be substantiated with references - can you please add link(s) and quote(s) that supports what you claimed?– B.LiuJun 12, 2019 at 8:46
Re: case 1, this is a common misconception: you are definitely bound by Vietnamese law even if you enter with a US passport. Jun 12, 2019 at 10:53