The purpose of the Add Form is to create a new row, there is no getting away from that.
To do what you want you should just use a details layout, then have your input components writing to user specific columns. Doing it this way will have the following benefits:
- You’ll just use a single row, over and over again
- You’ll be able to show the results in real time, without having to wait for the form to be submitted
- You can have two or more users interacting at the same time, without them tripping over each other
See also How do I create a custom form?