Is it possible to translate a multilingual JSON file in TMS, Trados Studio or Passolo ? 
 

"i18n": {
      "locales": [
        "en-US",
        "de-DE",
        "fr-FR"
      ],
      "definitions": {
        "plugin.name": {
          "en-US": "OpenManage™ Enterprise for VMware vCenter",
          "de-DE": "OpenManage™ Enterprise for VMware vCenter",
          "fr-FR": "OpenManage™ Enterprise for VMware vCenter"
        },
        "vm.action.label": {
          "en-US": "UI action",
          "de-DE": "UI Aktion",
          "fr-FR": "UI action"
        },

 

Unfortunately, Trados Studio, Passolo, nor TMS support multilingual JSON files and therefore TMS can't process such file without a customization.  More about JSON supported features can be found here.
For Trados Studio, there is a 3rd party filter plugin that could process certain formats of multilingual JSON files, but they are not supported by RWS nor will work in TMS
 

https://community.rws.com/product-groups/translationproductivity/passolo/f/forum/30853/multilingual-json-files-as-source
https://community.rws.com/product-groups/translationproductivity/f/studio/34080/multi-language-json-files
3rd party filter :
https://appstore.sdl.com/language/app/file-type-definition-for-json/561/