This is one of those things that – in hindsight – is fairly obvious, but which wasn’t until I was asked the question, and had to start thinking about it.
My user had switched computers, and part of that switch was to go for a multi-monitor setup. Said user uses a terminal server solution, to which he connects over RDP, for a lot of his work. Previously, this hadn’t been a problem, but now, he was annoyed by the fact that he could only go full screen in one monitor, effectively meaning that one of his monitors went unused for a large part of the time.
I started digging into his remote desktop connection settings. In the display tab, simply check the “Use all my monitors for the remote session” box, and connect to your server.