There are two CORDEX domain which cover the Caucasus (to some extent): region 8 and region 12. You can find more information here: https://cordex.org/domains/cordex-esd/ .
Provided you have a regional climate model available (some are freely available), a set of scientists and technicians who could set it up and run it and some computational resources, you can definitely produce your own simulations. For example Met Office (https://www.metoffice.gov.uk/research/applied/international/precis) and ICTP ( https://www.ictp.it/research/esp/models/regcm4.aspx) have a long tradition in helping groups all over the world setting up and running their own RCM.
