Offhand, I can't name one AM station I know to have an auxiliary site today. There must still be a few, but I am unfamiliar with any. This is, of course, a Scott Fybush question.
There are a few, even now. 50 kW WHAM right here in little old Rochester has a 12 kW transmitter at the site of sister station WHTK 1280, about eight miles to the east. It feeds one tower of WHTK's four-tower array, and WHTK has to operate nondirectionally from another tower at the site when WHAM is on from there. WOAI in San Antonio has a completely separate backup facility in Elmendorf, near the site it used from 1959 until the 1990s before it moved eastward to its current site. (But the aux site is new construction, built several years after the old Elmendorf site was dismantled.) WWL New Orleans has the ability to use the site of its sister station WWWL 1350.
More common, at least for the old-line 50 kW clears, is a second tower at the same site as the main transmitter, usually fed by a completely separate transmitter and transmission line. KFI, WSM, WFAN/WCBS, WMAQ/WBBM, WLW, WGN, CFZM/CJBC, WJR, WABC, WBAP, WCCO, WHAS, WLS, KDKA, WHO, KNX, WTIC (using the tower of former sister station WFSB-TV at the same site) all have such backup capacity.
And of course most directional AMs have at least some ability to stay on the air with one tower even if they lose others. At our WXXI 1370 here in Rochester, it would take a lot to silence the facility completely. There's generator backup if utility power goes out (which is VERY rare here), four towers to choose from should one be lost, a main Nautel XR6 transmitter that is almost completely internally redundant at full power (two separate power amplifier sleds, two power supplies), multiple STL paths (telco line, DSL, even feeding by FM HD2 if need be), and our old faithful 1955-vintage RCA BTA-5G that's ready to roar back into service when we need her.
I suppose if the building burned completely to the ground, we'd be off the air for a while... but Armstrong is only a 90-minute drive away in Syracuse and we could probably get our hands on an X1000 tuned to 1370 and get it set up in one of the doghouses at a tower base to get us back on the air within a few hours. Take down all four towers, too, and the next call would be to Entercom to see if we could put that X1000 a mile away at their AM site. (We'd do the same for them, of course.) And if they say no, we'd toss a longwire down from our FM/TV tower to the roof of the transmitter building...