Theoretically, yes it is possible. Practically, it will not be easy to get convincing results, but depending on the purpose, it might be worth to try.
The replacement person is very easy since you can film this second person in front of a green screen, which allows you to isolate this person from the background.
However, to get rid of the original person is a different story. I haven’t seen the footage, but I would expect that frame by frame masking (or cloning) is not a serious option and you would need the Boris RED plugin to do this in Vegas. But there is another Boris plugin, BCC Motion Key, that allows you to remove moving objects from a static background.
https://www.borisfx.com/units/motion_key.php
But since you want to remove only one person out of three, it will really depend on the footage whether you will manage. Motion key is part of the Vegas plugin Boris RED. If you don’t have this Boris RED plug-in, you can purchase Motion Key seperately, but then you will also need the Boris FX plugin in order to get it to work in Vegas. If you also have Adobes After Effects, you can use Motion Key without the need for Boris FX.
But like I said, the results will really depend on your footage.
Theo