Can I run two DVI cables to one monitor?

I have a monitor with a DVI input. Right now, it's hooked up to my PC via a DVI cable. I’m looking to buy a digital TV tuner and plug that into the same DVI port too.

Is this even possible? Does a DVI 2-in-1 adapter exist, maybe something with a switch to toggle between inputs?

Whatever. Just found out... I need a DVI switch (in case anyone else is looking). There's zero stock here in the States, and even on eBay—once you factor in shipping—they aren't cheap. Total cost is at least 200-$100... 😢