Which small, light aircraft are suitable for operating at very high elevations?
Yeah that location is going to present you with a lot of problems, most notably with density altitude and mountain flying.  This is also going to depend on the airports and runway lengths available as well as obstacle clearance altitudes for the area in question.  Most likely it's going to be a turbine powered aircraft which is pressurized for comfort and features good Short Takeoff and Landing (STOL) characteristics and soft field operations.

This question will probably be put on hold shortly, primarily because it is opinion based, but I would recommend a Quest Kodiak or a Pilatus PC-6 for the role due to meeting most of that criteria minus being non-pressurized.  You would just need to provide supplemental oxygen for the crew and passengers during the flight.  Another aircraft which would be recommended is a Pilatus PC-12 or the soon to be released Cessna Denali as they meet all of these needs albeit is a bit larger and less capable as a STOL aircraft.