I hope that maybe someone had a similar use case and has an idea how to solve it: I have content type that has an entity reference field to a vocabulary. With that I would like to achieve it to not only reference to the term itself in the manage display (in my case a country name), but also choose a certain value of a multiple value field of that term (one of the several historic names of that country). I created a hack with an additional list field in the content type (choose historic name 1, 2, 3...), but this is no good solution because as soon as I modify the order of the field items (e.g. because of adding one), the name is displayed wrongly all over the website. So there is the need to directly reference the field value of the referenced term itself.
You can do this in a custom field type based on the core reference field, adding a second property and dynamically filling the options of the select list depending on the first property.
For the multi-value part of your question a non-coding solution would be a paragraph containing both fields. Adding the dynamic behavior can then be done in a form alter hook or you can try Business Rules and adjust this recipe to your requirements: https://www.drupal.org/docs/8/modules/business-rules/advanced-usage/dependent-field
You achieve this with a multi-level taxonomy. Your country name would be the term on the top level and then the historic names would exist as children terms. You could write some code to infer the root term based on the historic term selected. Maybe as simple as having a second field on your entity and just populating it with the historic term's parent on entity save.