Is it possible to migrate data into multiple translations of entities?
I'm missing some informations for all understand your problem but, to migrate an object which have many translation you need:
Create the initial entity in the source language of your choose and add translation to this entity. For example, for a taxonomy term:

$default_language = "en";
$other_languages = ["fi", "sv"];

$term = \Drupal\taxonomy\Entity\Term::create([
  'vid' =&gt; 'my_vocabulary',
  'name' =&gt; $my_importer_object['name'][$default_language],
]);

$term-&gt;save();

foreach($other_languages as $language) {
  $term_object = [
    'vid' =&gt; 'my_vocabulary',
    'name' =&gt; $my_importer_object['name'][$language],
  ];
  $term-&gt;addTranslation($language, $term_object);

  $term-&gt;save();
}


Like it's a taxonomy term, it will be reference in your object like a entity references, with its tid. The link between translated version of the term and translated version of the node will be the language. If the term exist in the language of the node, Drupal 8 will used it automatically. If the term isn't translated in the language, Drupal will use the original language of the term, in which it had been initially created.