In 1:n/n:1 relationships when creating attribute maps, the system requires you to map the exact same type of field.
The system should also allow mappings where OptionSet is source, MultiOptionSet is target - after all the later is just an array of OptionSets. All it takes to convert from OptionSet to MultiOptionSet in JS are [array brackets] around the variable:

var result = JSON.parse(this.response); // parse JSON to object
var value = result["new_optionset"];
formContext.getAttribute("new_multioptionset").setValue([value]);