US 231 and US 431 meet each other a lot. 431 begins at 231 in Dothan AL, they’re multiplexed between Huntsville, AL and Fayetteville, TN, and then it ends in Owensboro, KY near US 231 (formerly at US 231 when both were routed through downtown).
Others that I can think of:
McRae, GA: US 341 and US 441
Saluda, SC: US 178 and US 378
US 301 and US 601 are multiplexed b/w Bamberg and Orangeburg, SC
US 301 and US 501 are multiplexed b/w Latta, SC and Rowland, NC
Conway, SC: US 501 and US 701
Murfreesboro, NC: US 158 and US 258
Burkeville, VA: US 360 and US 460
One oddity: US 301 and US 401 both go through Fayetteville, NC but don’t intersect!