(Updated 1/30/2020.) It is common for two different US routes to overlap (meaning they are concurrent along the same highway for a certain distance before splitting apart again).
It is less common for three (or even more) US routes to overlap. For example, traffic heading west from Cody, Wyoming, towards Yellowstone is on US 14, US 16, and US 20 (all at the same time).
Sometimes the two routes are signed in opposite directions. For example, heading west from Wytheville, Virginia, a short segment of interstate carries not only northbound I-81 and southbound I-77, but also northbound US 11 and southbound US 52. This arrangement is sometimes referred to as a "wrong-way overlap", or a "which-way overlap". These are a little more rare, but nothing to get too excited about.