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We could try to filter the WPLANG option locale (see e.g. this approach from the related list here on the right by @brasofilo, that's based on this one by @toscho ):

is_admin() && add_filter( 'locale', function( $locale )
{
    if( $lang = get_user_meta( get_current_user_id(), 'wpse_lang', true ) )
        $locale= sanitize_text_field( $lang );
    return $locale; 
} );    

where we check if the current user has the wpse_lang user meta key set, with values like is_IS, da_DK, ...

Then we could add the language selection for each user, on the user settings page.

There we could use the wp_dropdown_languages() function, with the get_available_languages() function, to display the select-box for available languages.

Here's a good example by @sanchothefat on how we can add custom user settings.

We can display the user language selection with:

function wpse_user_language( $user ) 
{
    $lang = get_user_meta( $user->ID, 'wpse_lang', true )
    ?>
    <table class="form-table">
        <tr>
            <th><?php _e( 'Admin Language' ); ?></th>
            <td>
            <?php
                 wp_dropdown_languages( 
                    [
                        'id'           => 'wpse_lang',
                        'name'         => 'wpse_lang',
                        'languages'    => get_available_languages(),
                        'translations' => [],
                        'selected'     => $lang,
                        'echo'         => 1,
                        'show_available_translations' => false,
                    ] 
                );
            ?>
            </td>
        </tr>
    </table>
    <?php
}
add_action( 'show_user_profile', 'wpse_user_language' );
add_action( 'edit_user_profile', 'wpse_user_language' );

and we can save it with:

function wpse_user_language_save( $user_id ) 
{
    if( current_user_can( 'edit_user', $user_id ) && isset( $_POST['wpse_lang'] ) )
        return update_user_meta( $user_id, 'wpse_lang', $_POST['wpse_lang'] );
    return false;
}
add_action( 'personal_options_update', 'wpse_user_language_save' );
add_action( 'edit_user_profile_update', 'wpse_user_language_save' );

Here's an example output: