What’s the setting range altimeters can handle?
There are actually multiple different answers depending on the specific type of altimeter system and what standard applies.  

The stand-alone altimeters in older aircraft and small GA aircraft (panel mounted "steam gauge") are certificated to SAE AS392C, Altimeter, Pressure Actuated Sensitive Type. The specified scale range is "at least 28.1 - 30.99 inches of Hg (946 - 1049 millibars)".  

This standard was updated in 2016 to require compliance with SAE AS8009C, Pressure Altitude Systems. Altimeters built to this standard have a specified range of 27.50 - 31.50 inches of Hg (931.3 to 1066.7 mb). 

Aircraft with "glass cockpits" use Air Data Computers certificated to SAE AS8002A, AIR DATA COMPUTER - MINIMUM PERFORMANCE STANDARD. Barometric corrected altitude correction is covered by Table 2, which defines a range of 22.00 - 30.98 inches of Hg or 745 - 1049 millibars.