You’d need a dock. HDMI alternate mode is probably what the USB-C port is being used for with that adapter (just a guess!) and I don’t think you can get two independent display outputs out of that.

<I>(short version: trying to figure out if the monitor is defective, or if there is some DVI incompatibility with this setup)</I><BR><BR>To connect a PC video card that has only a DVI-I Dual-Link ...

Macworld The more screen space you have the more efficiently you work apparently. So why not connect a second (or even a fifth) display to your Mac? In this article we help you identify which adapter ...