I'd like to practice harmony singing with one other person. After we get something that works, then allow others.

Jammr is not live so singing with another person will be impossible.

Please read the Tech Spport posts to understand how Jammr works.

WS

What about with headphones?

I don't think it is “impossible”, just different way of working. But yeah have a read through the instructions here https://jammr.net/faq.html or the Ninjam explanation I find works well to explain the concept:
“The NINJAM client records and streams synchronized intervals of music between participants. Just as the interval finishes recording, it begins playing on everyone else's client. So when you play through an interval, you're playing along with the previous interval of everybody else, and they're playing along with your previous interval. If this sounds pretty bizarre, it sort of is, until you get used to it, then it becomes pretty natural. In many ways, it can be more forgiving than a normal jam, because mistakes propagate differently. ”
The wiki page might also help: https://en.wikipedia.org/wiki/Ninjam
Its the same concept Jammr, I think its the same backend software…