Can several users control one Powered Up train using different devices?
As far as I know, this is not possible using the current stock firmware. The battery box can only pair with one device. The UI on the battery box is a single button, and for simplicity the device is either in a mode where it is looking for a device to pair with (flashing light) or already paired (solid light). There isn't a way to pair it with another device once it is already paired, and pressing the button while paired cancels the current pairing.

I'm hoping to put a train in my office before Christmas and it would
be great if multiple people could install the app and change the
speed.

There are ways to allow multiple people to control a device, but it will likely require a bit of software development.
Update
My students and I have been working on a possible solution to this problem that I wanted to share. We've created an open source project for the Raspberry Pi called twitch-powered-up that allows a LEGO model to be streamed from a webcam and controlled via simple natural language commands on Twitch chat. Here's the basic idea: